If you only play guitar and sing, you could look into the Blue Yeti, which is just a USB mic that plugs into anything.
Otherwise, like @YoBob said, one mic isn’t going to cut it, and frankly, 2 probably isn’t either if you want studio sound. I’d look into getting an audio interface and a few mics. This M-Audio is cheap and reliable, but if you’re recording a full band you could look at something like this Tascam, which is just loads of inputs for the price. I don’t have any microphone recommendations, as I’m a drummer and use fairly specialized mics when I get the chance, but Shure makes quality microphones, as does Blue.
As far as software goes, though, I would recommend using one and sticking with it, and I wouldn’t recommend Audacity. When recording music you really do get what you pay for, and unfortunately, you often have to pay a lot for good software. I’d look into Logic for software, as it’s really affordable (for a DAW) at $200 and will get you much further than Audacity. And GarageBand isn’t really good for much either.
The thing about buying audio software is that the first software you learn will have a hell of a learning curve, and by the time you actually end up mastering Audacity and figuring out how to get it to do exactly what you want, you’ll have outgrown it in scope and professionalism and will need to relearn a whole new, more professional software. So I’d bite the bullet and go with Logic if you’re serious about all of this.