Power amps:
Recommending a power amp is both easy and difficult. It's easy in that there are several good reliable brands like QSC, Crest, Crown, and Carvin, and you can find good choices from them at every sort of price range, power rating, and weight. It's difficult however to understand or explain why to choose one over another, either by itself or in relation to other equipment you already have. Plus you need to work with a certain amount of math in order to make smart decisions about matching amps and speaker cabs. This gets deep, so I'll try to keep things as simple as possible, but you will have to bear with a certain amount of technical explanation, it can't be avoided.  
Most PA-type power amps have two channels, meant for use in a stereo (left and right speakers) system, with two inputs and two outputs. Each channel is actually a separate power amp, operating completely independently of each other. However it is perfectly normal to use these PA units as a one-channel amp, either by leaving one side unconnected to anything, or by "bridging" the two channels. Bridging means connecting the channels in a specific way that turns them into one much higher-powered mono channel. Not all stereo amps can be bridged, and of those that can, each has its own method: some need a special cable, some use a particular output jack, some have a switch to engage. Be very careful about this, and read the manual closely. There are also some one-channel power amps, usually made by bass amp companies.
 
Although wattage isn't the most important spec to look at, you should start your power amp search with the published wattage ratings of the speaker cabs you'll be using. The question of how much wattage you "need" or how much is "safe" is very complicated and arguable; for now, just to keep things simple, use the nominal ratings of the cabs as your maximum for wattage from the power amp. For example if you have two 8-ohm cabs and each is rated for 400 W, and you're hooking one up to each side of a two-channel power amp, then look for the amp's specs to say something like "400 W per channel at 8 ohms". A smaller amount is fine. You may be thinking more wattage is better, but trust me for now--wattage does not equal loudness.  
If you're using only one amp channel, or bridging the channels, then you will connect your cabs together in a chain off of one output from the amp. This usually means the cabs are "in parallel" (a specific electrical relationship), because the pair of jacks on most cabs are internally wired in parallel. It doesn't matter if you hook the cabs up in a chain from one to the next, which you'd think is in series--the electrical connections via the jack plate are still in parallel. Connecting two 8-ohm cabs this way will make a 4 ohm total load, and if each of them is rated for 400 W then together they should be able to handle up to 800 W. So you would look for the power amp specs to say "800 W at 4 ohms bridged" or "800W per channel at 4 ohms". If one of the cabs is rated for more power than the other, then the safest bet is to forget that higher rating, and pretend they both have the lower rating. If you hook a 200W cab up with an 800 W cab, that does NOT mean you can safely use a 1000 W amp, because half the power will go to the 200 W one, resulting in blown speakers.  
The math for combining speaker loads goes like this: take your speaker ratings and flip them into a fraction, so 8 ohms becomes 1/8, 16 becomes 1/16, and 4 becomes 1/4. Now add them, so for example 1/8 + 1/4 = 3/8. Now flip it back over, and you get the total load. 3/8 becomes 8/3 which is 2 and 2/3, so 8 ohms plus 4 ohms makes a 2.67 ohm total load. Two 8-ohm cabs in parallel make a 4 ohm total load, two 4-ohm cabs make a 2 ohm load. In the specs for most power amps it will say "minimum load 4 ohms", and this means the amp will burn up if you connect it to a load of 2 or 2.67 ohms. So if you intend to make connections like that, be absolutely sure the power amp you buy says it can handle a 2 ohm minimum load. This warning is for each channel (or bridged)--there is nothing wrong with using two 4-ohm cabs where one is on each side of a stereo power amp, because each amp channel is independent, and those speakers are not connected to each other. It's also quite safe to use one ohm load on one channel and a different ohm load on a separate channel--all that will happen is each side will get different amounts of wattage.  
Important note: the volume or gain knobs on a power amp do not control the wattage. A power amp is capable of putting out its maximum wattage at almost any position of the volume knobs (above zero). This is because the volume knobs turn down the level of the signal going into the actual power gain stage, but they do not limit the output of that stage. That output stage is always at its full potential, ready to multiply whatever you feed it, up to its peak ability. Turning the knob down 50% just means you turned the preamp signal down by some amount before it gets amplified. However a 500 W amp is not putting out 500 W all the time, that number is just the maximum it can reach before distorting "too much" (by the standards of the amp designer). The power output is a multiplication of your input, so a quiet note produces a lower amount of wattage and a loud note produces a higher amount of wattage, and a really big transient spike will push the amp to its maximum wattage or beyond, with some distortion.  
Next we consider size and weight. Most racked power amps are 2 rack spaces (2RU, 3.5") tall. There are a few 1RU ones, but they tend to be twice as deep front-to-back as the 2RU ones, and weigh the same, so there's no real benefit to hunting for one of those. Plus some 1RU power amps have a problem with overheating, requiring you to leave an empty rack space above them for ventilation, so they end up taking 2RU anyway. If you need the smaller size, consider using a micro amp head instead of a two-channel power amp. This is what I do, myself. With most amp heads, if you plug into the "power amp in" or "effects loop return" jacks, this allows you to bypass the built-in preamp, and use the head as just a plain power amp. With the normal 2RU amps I look for a shallow depth, less than 11" or so front-to-back.  
Amps have gotten incredibly light-weight in recent years, but some people still feel they get a heavier tone from a heavier amp. This is an area where opinions are divided, and it's tricky to prove scientifically whether one power amp sounds the same or different from another. You'll see a lot of people claim that they did a rigorous A/B listening test and came up with a definite result, but if you inquire further you'll usually find that their test was not scientific at all, and missed some really important factors. You'll see people complaining that the lightweight "digital" amps are wimpy and "sound too digital", even though the sad fact is that amp manufacturers use the word digital to mean all kinds of different (even totally unrelated) things, so as consumers we are stuck with a bunch of misunderstandings about what we heard from an amp. Is it "digital" because of some signal processing (DSP), or because it uses a switch-mode power supply, or because of a switching (Class D) amplification stage? What do any of those mean about tone, or about each other? It's a mistake to make sweeping generalizations about how all these systems perform. Personally I choose the lightweight option because the benefit of lighter weight is immediately obvious and inarguable, whereas all the other qualities people get hung up on may not be all that significant at the gig, and may even be imaginary.  
Power amps made by bass amp companies are usually designed with some tone coloration (preset internal EQ shaping, for example) that represents the "flavor" of that bass amp brand. But power amps meant for PA systems are always designed to not color your tone at all. How well they achieve that goal is open to debate. A lot of what we perceive as tonal difference between amps has to do with how they behave when driven into clipping with big signal peaks. Some units are clean up to a point, and then sound terrible when distorting. Others may ease into some soft clipping when you push them, and they will sound both louder and more musical. It may not even sound like clipping at all, it may just sound like "fullness" or "strength". But it's actually not easy to identify which power amp will have good-sounding clipping behavior, so this is the one area where it is worth paying attention to people's opinions about the tone of an amp. Just don't get caught on the slippery slope going from "sounds great when pushed hard" to "sounds better at any level because of premium components, traditional large power supply, etc." It is easy to start off with good science and end up with voodoo and fantasy.  
Another thing that affects how we hear the tone of a power amp is whether its input sensitivity is a good match for the output levels of your preamp. If you A/B compare any two power amps, using the same preamp and the same settings, odds are good that one of the power amps will sound better than the other! But you will almost always find that the better-sounding one had a lower input sensitivity rating, meaning it was driven more strongly by the preamp, giving you a gutsier sound. But that doesn't mean it inherently sounds better than the other power amp. It just means the other power amp needed to be driven by a stronger input signal, to get the same quality of gutsy tone. This is the biggest, most common mistake people make when they try to compare amps. Fortunately for you, this one is easy to solve! Just look in the spec sheet, and choose an amp with a low input sensitivity rating like 0.7 volts or 1.0 volts, as those are ideal and will be driven easily by any racked preamp. With a sensitivity like 1.25 V, it's a little bit of a gamble, needing a stronger-than-average preamp output. Avoid any power amp with a sensitivity rating as high as 1.4 or 1.5 V, unless you know for a fact that your preamp has very high output levels.  
The input jacks may be balanced (XLR) or unbalanced (1/4"), or both with a combo jack. The balanced input is usually the better choice, because in many cases the power amp will see a 6 dB higher signal at that input, allowing it to be driven more strongly by the preamp. Unfortunately a majority of guitar and bass preamps have only an unbalanced 1/4" line-level output jack; their XLR DI jack usually puts out a low-level signal meant for connection to the mic input of a mixer, not a power amp. This is an accursed gap of failure to communicate between the manufacturers of guitar gear and the manufacturers of power amps. One solution is to use a "channel strip" preamp meant for recording studios, instead of a guitar/bass preamp, because most channel strips have a balanced line-level output. Another solution is to insert a unity-gain active (powered) balancing box between the preamp and the power amp. Yet another solution is to add a rack compressor or EQ that can boost the output of the preamp. But the simplest solution, to avoid adding more gear, is to look for a power amp with a low input sensitivity rating, as that will make the 6 dB benefit of the balanced connection unnecessary. In most other situations the point of balanced cabling is to reduce noise, but in the back of a rack rig the cables are usually short enough that even unbalanced ones don't pick up much noise.  
There are three main types of output jacks for connecting to the speaker cabs: 1/4", banana, and Neutrik Speakon. Even though the 1/4" is extremely common and people have been using it worldwide for many years, it is the lowest quality, lowest reliability, and lowest safety of the three. It only allows a tiny point of contact between the plug tip and the jack, which can easily be degraded by dirt, corrosion, or a bent contact spring, resulting in poor sound quality. It is too easy to mix up a 1/4" speaker cable with a guitar cable, and using a guitar cable this way can result in overheating and possibly destroying your amp. 1/4" plugs should ideally not be used with high-wattage (like over 300 W) rigs, again due to overheating. Both banana and Speakon plugs solve all of those problems. Speakons have some additional benefits: they lock into place so they won't pull out accidentally; they don't have any exposed wire or metal that could shock you or short out against the jack plate; they only go in one way, so you won't accidentally plug in the wrong polarity (which can happen with bananas); and they are easy to fix or rewire using just a screwdriver, no soldering. But banana plugs are still an excellent choice, there's no need to avoid them. Even if your speaker cabs have only 1/4" plugs, I strongly recommend you choose a power amp with either bananas or Speakons, and buy (or make) a speaker cable that has the better plug on the amp end and the 1/4" on the speaker end. Better yet, take the 1/4" jacks out of your speaker cabs, and replace them with bananas or Speakons--it's an easy project.  
When reading power amp reviews, you can mostly ignore comments about tone, but you should pay close attention to comments about reliability. Does the amp overheat, shut down, act funny when used at certain venues, or trouble its owner in any way? How long has the reviewer been using the amp, and in what types of gigs? Has it needed servicing, and how difficult was it to get service from the manufacturer? How long is the warranty, and how does the company treat you once the warranty has expired? How easy is it to clean dust out of the fans and vents? How did the amp perform after it was dropped from a loading dock onto the concrete?  
You may be looking at features in a power amp such as a crossover, low-cut filter, EQ, or DSP. For most people these features are totally unnecessary, and I do not recommend choosing a power amp just because it has more stuff. Now clearly if you really know you need a certain function, then of course you should shop for that specific function. For anyone else though, who isn't sure exactly what they need, you should keep it simple and avoid focusing on those extras. A low-cut (high-pass) filter can be very useful, but you'll need to study up on the specific parameters of the filter versus your particular needs, rather than making a purchase based on an assumption. At a minimum, make sure the filter is easy to switch on and off.  
Lastly let's talk about wattage versus loudness or volume. Obviously you need watts to move speakers and produce sound, so watts are a necessary part of amp loudness. But it is a HUGE mistake to assume that more watts = more loudness, or that they are even directly related. First, our ears don't hear all frequencies the same way, so it takes different amounts of power to get different frequencies up to the same perceived volume. This is why a guitarist can be screaming loud with a 60 W amp, while a bassist may want ten times as much wattage. This also means your EQ settings have a major impact on how loud your amp sounds. Secondly, your speakers have to be able to use that wattage effectively and efficiently, without ripping apart. If your speakers are inefficient, you need more wattage to get loud, but then if they are not physically able to handle the excursion demands from that wattage, they'll be destroyed.  
You will almost always get a much more effective boost in volume from adding speakers rather than increasing wattage. This is partly because the increased speaker area will move more air, and partly because the increased number of drivers will better distribute the physical strain. Whereas if you just increase wattage, your speakers will not have any more ability to move air than they did before, and they won't be able to cope with the extra strain as you demand that they work harder. Bear in mind too that the wattage rating on any speaker cab is just the amount it can handle at a certain frequency before melting and burning. Most speaker cabs will start to "fart out" and distort, especially with low frequencies, long before reaching their rated wattage.  
You will see comments on the web, even coming from supposedly authoritative sources, saying your amp should have much more wattage than the speaker ratings for "increased headroom", or to avoid "underpowering" the speakers. Both of those are false. The first one blatantly ignores the problem of whether the speakers can handle the power. Be sure to check out my FAQ article on headroom for more explanation. The second is just an old myth--anyone who tells you to avoid underpowering your speakers has gotten terribly confused by bad science and old wives' tales. The reality is if you want to avoid blowing your speakers, you want to avoid pumping too much power into them, and one good way to do that is to use a power amp that is rated for less wattage than the speakers. If you want more volume, add more speakers, which will then probably allow you to use more wattage.  
So in summary, when buying a power amp you should look for reliability; look for only as much wattage as your speakers can safely handle; look for a low input sensitivity rating; look for banana or Speakon jacks; and as long as you've got all that, then go ahead and look for light weight and small size.
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