I actually find that all my mics tend to record my computer well- as much as I'd like to keep the annoying fan noise OUT of the recording....
Welcome to the board!
Check out the mics in the Studio Projects line for some well liked (and well hated) low cost options. The MXL 603s is another favorite for instrument recordings, though I think MXL just came out with an improvement- hopefully someone will happen along who's been paying closer attention than I.
The stalwart beginner-to-advanced mic of choice seems to be the Shure SM57- it'll grow with you and sound better with better gear. Its the rare mic that is a frequent first purchase and still used regularly 20 years later. Also the standard mic for guitar cabs. Not so hot on acoustics, except for live shows. Can even be used for a kick drum in a pinch.
Without having a better idea of what you are doing and what other equipment you may have, though, its hard to be more specific. For example, if you have no other preamps or audio interfaces other than the little plug on your computer... nothing is going to sound all that great- maybe concider something like
the BLUE Snow Ball for the cheapest option? I have no idea how it sounds, but *nothing* is going to work well with an on-board sound card and the Snow Ball is USB.
Best I can do for now. I hope that was at least marginally helpful.
-C
Edit: Whoops- I guess the Snowball hasn't been released, yet. Oh, well.