OK I had to chime in on this one.
Personally I use ProTools 10 for the primary DAW in my studio. But that would be way overkill for what it sounds like you want to do. I also use Ableton Live 8 and Reaper 4 to rewire into ProTools.
I really can't speak to audacity, but I know a lot on here seem to use and like it. The price is right.
I would recommend that you look at the website and capabilities. Be sure you understand what kind of interface you will need.
If you don't mind spending a few dollars, Reaper 4 is about $60 for non commercial. Win doze or Mac, and it will run in 64 bit mode!. You can get a fairly inexpensive interface from 1 to 8 mic preamps for $250 to $400.
Of course if you are up to it, you could go with the Avid Fast Track C400 h
ttp://www.musiciansfriend.com/pro-audio/avid-fast-track-c400 which is a 4 X 6 USB interface (windows or Mac) and has on board DSP. (The DSP is really important if you want to use software effects.) For about $150 AND that comes with ProTools SE which is basically lite version of ProTools, BUT it is also and upgrade path if you choose to go to the full version at some point.
I admit, I am a ProTools fan, so that solution is what I recommend. ProTools is the most widely used DAW software in the industry, so you will be able to take your tracks to any major studio to work with. Then we can all say "I knew Dave way back before he became a star ;D".