There's a lot of different mics you can get quite cheap (or at least relatively cheap), and I agree with Jamie that Røde is definately a brand to check out. There's also SE Electronics, which I think could be interesting. If you, as Jamie says, want to record for instance drums, there's kits with dynamic mics from AKG that works great.
Concerning software, they can all have different qualities, for instance Pro Tools is originally meant for audio editing to films so it has some strengths in that area, Logic has a really intuitive music writing interface, Ableton is great at beat making. But they all work, and they all essentially do the same thing. So perhaps you are perfectly comfortable with Audacity, or maybe some other software is more your style. But I think it's important to remember that there's no right or wrong here, only what works for you.
Most softwares also have a free trial, so I'd recommend taking the time to try some different ones out before spending money on it.
Personally, I like hopping between Logic, Pro Tools and Cubase depending on what I'm doing.
Happy hunting!
P.S It would be fun to know what you decide in the end