Great idea.
Welcome to the crazy world of live band, multichannel recording...
I multi-track record most of my bands rehearsals and mix-down/burn everyone their own personal practice CD with all parts but their own.
The recorder I use is probably beyond your budget or needs, but this one will record all 24 channels (@24 bit) simultaneously for hours and hours on end:
http://www.alesis.com/product.php?id=1
Mine is just a standalone recorder, so I also need external mic preamps of some sort, and a way to mix down and burn CDs.
(the rest of my recording gear is listed in my profile)
I'd imagine your also going to get into a fairly expensive setup to do 8 to 24 channels of simultaneous recording with a computer, but that's definitely an option.
I'll let the others comment on multi-track computer recording.
There's some fairly inexpensive (standalone) 8-track recorder/mixers on the market that should work great for your needs.
Here's a bunch:
http://www.google.com/search?sourcei...track+recorder
(used ones):
http://www.google.com/search?sourcei...track+recorder
(Note: some will record all channels simultaneously, and some only do two at a time)
For a really cheap price, you could just buy an older used cassette 4 or 8-track recorder (with built in preamps and mixer) that would have 2 stereo outputs to run to your computer for CD burning.
Here's a few:
http://www.google.com/search?hl=en&r...ssette&spell=1
There's a few different options for ya, good luck.