I use both Audacity and Reaper, and I agree with Boydie. I learned Audacity first and used to use Reaper only occasionally for anything. But I found myself gradually moving more and more to Reaper and now I rarely use Audacity. The main reason is how Audacity [doesn't exactly] handle effects like reverb, etc. Once you apply them, you can't just turn them back off. Frustrating.
Reaper is low-priced PLUS you can try it for 60 days before you pay. PLUS, if you don't pay in 60 days, it keeps right on working. It took me longer than 60 days to decide I really was going to use it. A lot longer.
Oh, and since you already have Ableton, you could keep practicing with that instead of downloading Reaper. Just keep trying it out a little at time, if you need to. If you get frustrated, export the files to WAVs, load them in Audacity and continue in the familiar environment.
Oh, another thing about Audacity that makes me crazy--when you delete a piece of a track, everything to the right jumps to the left to fill in the hole. Ugh! In Reaper it stays where it belongs. I don't know about Ableton.
My two cents' worth.
Vicki