The equipment you need depends on your situation. Are you looking to record live shows, or one track at a time to a PC in a home studio?
Most likely, it will be the later to start. For that, you will need a fairly decent PC with a 2GHz or better processor and 1GB or more of RAM. And plenty of hard drive space for the wav files that most programs use. You will also need a pretty decent soundcard with a line in (which most have a 1/8 inch jack for this) or one of the USB/Firewire devices. You will also need a couple of dynamic microphones for recording instruments, one or two condensers, a preamp/and or mixer, stands, and cables. You will also need a monitoring system of some sort. You may be able to get away with using your PC speakers
Now, a lot of people are very opinionated about what brand of equipment to use. Don't let this sway you from buying something that works for you, and most importantly, what you can afford. You don't need to go out and buy a $400 condenser mic to start. Nady makes some very affordable mics that work pretty well. The same holds true for mixers and other gear. To start, it will take a pretty fair amount of cash to buy everything you need at once. Use some of your live gear (cables, mics, stands, a mixer) if you can to help with this. And don't be afraid to try some lower end stuff at first, just do your homework to make sure you are not getting a lemon.
I started with 2 tape decks, a couple of Radio Shack mics, and a 6 channel DJ mixer, a couple of 20 watt PAs and a pair of indoor/outdoor speakers. The whole set up cost me a few hundred dollars at the time. Over time I upgraded here and there, but today, you should be able to start off a little more advanced for about the same investment.