Also, how would I record each channel directly to mix later?
This is where things start to get more expensive. There are at least two parts to your question: (1) how to get the individual channels, and (2) how to record them. Let's look at these separately.
How to best get the individual channels depends a lot on the sound board that the band/venue uses. Some of the better mixers have line outs for each channel; ideally, they can be switched between pre-fader or post-fader. What that means is that you can choose whether fader movements by the sound guy during the performance affect your recording or not. If at all possible, I'd go for pre-fader - otherwise, some changes made by the sound guy (which you may or may not have in your final mix) will have to be compensated for in your mix. This scenario is also convenient in that you don't have to invest in high-quality pre-amps yourself, because you will be using the ones in the venue's sound board - hopefully of good quality. All you need is an audio interface capable of capturing the desired number of channels (line-in), and of course one audio cable per channel (typically with 1/4" phone plugs).
If the sound board doesn't have line outs, it gets more tricky. In theory, you could put each instrument/voice by itself on one aux channel and record that, but aux channels are limited in number, so you will have to group inputs and mix them during the recording, which kind of defeats the purpose. Still, this can give you more options during post production than just recording a stereo mix.
Another way would be to use splitters for all the inputs into the sound board. This gives you the same flexibility as the first solution (individual line outs), but at a higher expense because you'll need a splitters for each channel - plus you need to worry about pre-amps, who provides phantom power, etc.
Now let's look at part two: how to record all these channels. The MicroTrack mentioned by Sesshi is not a bad device - I have one myself, use it as a backup recorder - but to record a live music performance and mix it in post you'll need to record way more channels. There are FireWire audio interfaces for laptops that can help you - which is what I used to do until one night the laptop just decided to stop recording halfway through the event. Looking for a more reliable solution, I asked around and was pointed to a PC-less solution consisting of a recording mixer (with line-outs) and a multi-track recorder. I ended up buying a Soundcraft FX-16 mixer and a 24-track harddisk-based recorder, the Alesis ADAT HD24. I installed both in a rack for easy transportation, and I couldn't be happier with the solution. Not cheap, but it gives me tremendous flexibility and very high recording quality.
- Martin