As of now (August 2008) all the tracks that you hear on my website, http://dccardwell.com, http://facebook.com/dccardwell etc, were recorded with a much simpler set-up. I used a very basic computer and recorded into a consumer "Soundblaster Live" soundcard, which you can get for only a few dollars. You can even use a built-in soundcard, but when I've tried those they're a bit noisy, especially if you're not very careful about levels.
I used a little Behringer 12-input mixer between the mics and the soundcard - with the Soundblaster I could only record one or two tracks at a time, so I could have got away with one of their very tiny mixers. You can get decent condenser mics now for very little money, like the Behringer C2 pair, which are good for acoustic guitar and other acoustic instruments, or the B1 large diaphragm one. Condenser mics are more natural sounding than dynamic mics, but you need phantom power in your mixer, which I think even the cheapest smallest Behringer ones have.
I also got a couple of nice cheap Samson condenser mics recently, reduced to AU$59 each, so very affordable. Fine for vocals and just about everything else.
But ordinary dynamic mics will do OK for most things too. I used a cheap Behringer one for the vocals on my song "Tom Is Everybody's Friend" and it's actually the best sounding vocal I have, I think.
You don't need any effects units (reverb, compression, delay etc) as that can all be done in your software.
For software I use Adobe Audition which is not too expensive and hugely versatile. I love it. But the freeware program Audacity (www.audacity.sourceforge.net) is a perfectly functional multitrack recording program which will work fine, and is actually easier to use for the novice.
A lot of people go the Pro Tools LE (Lite) route. Pro Tools is the industry standard software but for it you need to use dedicated hardware, eg by M-Audio or Digidesign. So that rules out using your computer's built-in soundcard or a consumer gaming card like the Soundblaster.
So, you see I did a lot with very little! Now, with my new gear, I'm happy to be able to record more than two channels at once. But if you want to record all the parts yourself a simple set-up is fine.