This can be very simple and you can get great results with minimal equipment. I recorded a 4 member group for a Christmas album project and it turned out really well, regardless of the cheap equipment I used.
What I'd do is this:
Try to find a used 12 channel mixer on eBay. Mackie is preferable, although almost any brand will do. There are a few mixer names to avoid, in my personal opinion. They would include Peavey, Behringer, Fender and Alesis. You want something with durable, quality preamps, gain controls and faders. Onboard EQ is nice, but not always a necessity.
Anyway, you're gonna want at least 4 mics. You could actually probably get away with 2 or 3 mics, but I strongly recommend 1 for each singer. Now, since I imagine each one of the singers has a different range, I would tend to think that 4 mics of the same brand would do fine. However, try different mics with your group...go shopping around and see how many mics you can audition. Large diaphragm condenser mics will sound best for acapella vocals. There's a lot of good things being said about
the Studio Projects C1 condenser... I believe it runs for $200 or more. The Marshall V67 is another popular candidate which can be had for as little as $170 or less sometimes. (gotta look thru ebay often)
The AT3525 by Audio-Technica is not a bad mic for the money.
www.8thstreet.com sells them for $150 new. I wouldn't recommend it for all vocalists, but you might want to audition them and see how they sound on each one of your guys. It would save you around $200 if you buy 4 of them instead of the higher priced, large diaphragm condenser mics, but I wouldn't encourage you to skimp on quality, even if more money needs to be shelled out. It's worth it to do things right the first time if you can.
Acapella performances will always sound better with reverb. You can get good reverb for under $200. Lexicon makes some fine models. the MPX-100 comes to mind. Try to find a used one on eBay, but be warned: I wouldn't pay more than $160 for a used MPX-100. Don't overdo it, either. You just need some ambience to add character to the performance; not a muddying of the sound.
Good cables are worth good money. Cheap cables will inevitably go bad, and the result won't be pretty. Ask around and get opinions from credible people who know their stuff, and make an informed decision when you make your purchase.
An alternative to the mixer idea might be a higher-end soundcard. I believe there are some decent products which will accomodate XLR inputs and will interface with your computer for multitrack recording.
Anyway, it's late, and as a result, I might start saying stupid things without realizing it...so it's off to bed.
Isaiah