Geeq,
I cant think of a more general way to ask your question. What you are looking for seems to be an array of answers. I will take a shot, but you might want to try other approaches to finding this stuff. You might want to search the board on the various devices to see what others are concerned with.
The other way to go about this is to define what you want to be able to do and ask for suggestions as to what you might need within a budget.
Here are some short answers to your question.
A compressor decreases the dynamic range of a musical signal allowing recording of a source that has loud peaks without having to turn it down. It's like having a guy with really fast ears and fingers to ride the input levels and turn down only when you have to. Limiters are similar but are more extreme in the amount of gain reduction. Lots of compressor units come with what is called a gate that lowers the input level when there is not real signal present reducing noise.
Crossovers are used primarily for PA systems dividing the highs mids and lows so that individual amplifiers can power speakers (drivers) with signals that they best produce. To over simplify this lows go the big speakers and the highs go to the little ones. Lows going to smaller drivers can blow them. Often a two way or three way speaker cabinet will have a crossover built in.
I don’t know what you mean by "SOUND SYSTEM IMPROVERS", but if you are on a budget the first thing to do is spend your money on good mics, a good mixer and a good recorder. Each device you ad between the source and the mix down can add noise, so use them sparingly.
There is no amount of magic signal processors that will make a bad source sound good IMHO. You need players that are well prepared and have a good sound already. A good room makes a huge difference as well.
One thing that people overlook that seems to work quite well is recording music live to a nice pair of mikes, pre-amps and a two track recorder such as a DAT or a CD recorder or both.
Rane corporation has a bunch of web publicaions on almost any audio topic you might be interested in.
http://www.rane.com/library.html
You might want to start here.
http://www.rane.com/pdf/live97.pdf
good luck,
john
