While I'm a huge supporter and love Reaper, it's timecode support does still lack a little bit. It also doesn't have OMF import capabilities. With v4 there are going to be some huge improvements in that area. So I'd have to say for professional scale work (and in regards to this I'm only speaking of conforming and surround mixing), then you're going to need Pro Tools or Nuendo. Reaper's video support is just fine, you just have to use the proper video format for the operating system you are on (if not you get a lot of issues that seem to throw most people off initially).
I should also add that I do a lot of sound design in Reaper and prefer working in it as much as possible (since it's an amazing sound design environment) and then import my material into Pro Tools when I need to conform and mix. In the past 6 months I've also begun doing smaller projects completely in Reaper and find that it works just fine if you don't need surround or if timecode or OMF import is not really necessary or is negligible.
So I'd have to say that if you can't get Pro Tools or Nuendo now, then it's a great place to start practicing, even do smaller/shorter projects on and will become an invaluable tool later on as well. In fact... if not for the few things it's lacking in necessary audio post functions I would have ditched Pro Tools long ago.
Besides, with Reaper they work on the honor system (expect you to do the right thing and pay after the 30 days has passed) and they offer a fully functional un-expiring "demo" of their software and their personal use license is cheap. Which will give you enough time to decide whether you want to use it. I've been using it for close to 3 years (using Pro Tools for 14yrs) and I only grow to love Reaper more and more. Also, you will be able to continue to use Audacity as your audio editor in conjunction with Reaper, so your learning curve won't be as hard at first while you wrap your head around using a DAW for audio post and sound design.