If you're running 64bit Windows, run 64bit Reaper, although I didn't see any difference between the two on my old laptop. All my newer versions are 64bit. The only oddity might be some newer 64bit VSTs might not run correctly on 32 bit systems. Reaper usually bridges between the two, but sometimes there could be a problem.
You have a 64 bit OS, so that version should be more efficient.
All you projects should move seamlessly as well.