Definitely purchase a good mic or two. Study up on the types of mics and decide which is best for your needs. Shop around and test 'em out. Shures, mentioned by Glenoled, are a great choice - good quality, low price.
If you have a powerful, computer I strongly recommend Cakewalk. It’s a professional audio/video software package that’ll give you almost unlimited digital tracks and a nice suite of effects for mixing. That said, it has limitations. The reverb and compression are substandard (for me) and you really need Soundforge or another like package.
If your computer is slow (or you only need a couple of tracks), you might want to stick with one of the many analog multi-trackers Gleno suggested - though I’d stay away from the little “portable” 4 tracks due to their limitations.
To produce studio-quality recordings, you’ll need a LOT of money. You’ll want better mics, a powerful reliable amplifier and a 30-band stereo EQ, professional reverb & compression units, high-end monitors and headphones for playback and mixing, a good dual tape deck and a 2x or faster CD-burner.
I just finished my band’s demo - this is what we used:
Drum tracks recorded using four Shure mics through a DOD stereo 8-channel powered mixer into a Yamaha MT-4X.
Tape transferred to Cakewalk on the computer. Acoustic Research monitors and Sony Headphones through a Sansui Amp.
Bass, Guitar, Vocals & FX recorded direct into Cakewalk.
All necessary punch-ins and re-takes recorded as separate tracks.
Mixing done in Cakewalk and Soundforge.
Pressed to CD in a 2x HP burner.
The demo sounds pretty damn good, but the weak link was the mics and the quality of vocal effects. For a demo, though, it’s spectacular.
Due to the nature of this site, I’m not going to post a link, but there are sites out there where you can download cracked versions of all the sofware listed above, thereby saving a starving musician hundreds of dollars. To save further money you can rent equipment instead of purchasing if your project is short.
Yet to be reconciled with the reality of the dark for a moment, I go on wandering from dream to dream.