Shure SM58 is the best microphone in the business. Durable, dependable, clean sound, and genuinely the best microphone for general-purpose use you can find. It's $99 on Musician's Friend. For miking an instrument, the Shure SM57. Accept no substitutes. If you can spend more on a proper microphone, do, but for $99 each, the SM58 and SM57 are as good as you'll need for amateur recordings.
As for software... define cheap? Sony makes some good software, and Sonar is really good for audio recording as well. Cool Edit Pro was my top choice, but they were bought out by Adobe and genuinely suck now :/
Agent Dink and I are in the process of making a website about building a home recording studio. For about $5000 you can record a full band with quality equalling a professional recording studio, or in the very least getting as close to professional as humanly possible. When we finish that site I'll put something up on TGC about it.
If that's an acoustic-electric, you should be putting it through a direct-box. Also, you should be recording the tracks independently... do your percussion (I hear hats in the background) first, then play guitar on a separate track, then sing without holding the instrument. Mixdown into a single track and you'll maximize your audio quality and the timing will be more precise. Drop me a line on Yahoo Messenger or via email and I can walk you through stuff, I was a DJ at a radio station for several years and I've recorded every band I've been in, so I'm decent with audio stuff
