If you want to do it on the cheap, then with $600, you shouldn't have a problem
You've probably got a relatively generic soundcard - Sound Blaster Live or something similar. I'm assuming that you're running Win 95 or 98. You can find out what sound card you've got by going to the Control Panel (Start -> Settings -> Control Panel), and clicking on the Devices icon. This displays the hierarchy of all the bits in your computer. Look at two sections - 'Sound, MIDI and Games' I think it's called, or sometimes things appear in the 'Other' section.
To do something decent, you need a reasonable sound card (for starting out, a Sound Blaster Live is fine). You'll also need one or two mics, depending how you want to record. I'll get cained for saying this, but Shure SM57's or SM58's will be plenty when you start out. Obviously there are better mics, but if you're starting out, these mics will suffice.
For software, get n-Tracks ($35 and you can buy it on-line). It's brilliant software, even more so for the price. Go to
www.fasoft.com for a peek (you can get a demo for free). There is other software out there, but it is much more expensive. For $35, you can't go wrong.
So far, you're up for about $200 if you get 2 mics. That leaves $400 - and the options start setting in. You could get a number of things - a decent condenser mic like a Rode (I think they're around $300USD - I'm from out of town, so I'm not too sure), a nice tube preamp (Art Tube MP), a compressor (Behringer Composer for example), or a proper prosumer recording sound card (gadgetlabs, echo, aardvark etc.). So many options, so little time.
I guess if you're just starting out, get the basics (mic and software), play around for a few weeks, surf this and other sites, and then you'll be in a better position to decide what you really need. The mic and software will always be useful.
Cruise through the archives to see what you can find.
Good luck
- gaffa