Hi Bee: That was one of my first questions on Mudcat and I've learned a lot here. Since you're going the computer route, you will need a Large Diaphragm Microphone and an Audio interface to get digital sound into your computer. Forget the 1/8" inch jack. It will create hiss. I can pm you with some links if you like but you can expect to spend $200 just to get started.
Most folks around here, swear by Audacity but it's too complicated for the likes of me so I forked out $50 for Mixcraft.
The best example of sound quality for a solo track, with my set up would probably be "The Bold Tommy Makem" or "The Convict of Clomnel" at http://www.myspace.com/folksingerjim
You can buy a decent mic online, for around $100 and a small audio interface for around the same price but one of the more advanced audio interfaces at around $250 will give you phantom power, two inputs and various bells and whistles which you will find a use for as you progress. The latter purchase should be made at a local music shop in case of compatibility issues. (which do happen)
Welcome to the wonderful world of microphonology.
Cheers!
Jim