Reaper is very track focused. If you were looking under the file menu, all of those options are dedicated to the files created from your project. There are a number of ways to import external audio, though. The easiest is to just drag the audio file from your computer into the Reaper track panel. Reaper will create a new track for you and insert the audio. You can also use the Import->Media File menu. Or the media explorer.
I know you guys are comfortable with Audacity, but it is a toy, and I mean that in the nicest possible way. There is nothing it can do that Reaper can't, and there are about a thousand things Reaper can do that it can't, and it does everything better. Reaper is a professional audio tool on par with ProTools. It is more complex than Audacity simply because it does way more that Audacity. Russ, for someone doing the quality of work you are doing, I honestly believe it is holding you back. Even if you don't like Reaper, there are literally dozens of better options out there. Logic, CubeBase, Cakewalk.... They can all do live VST, native MIDI sequencing, non-destructive punch-in/out, everything that you would expect in a professional workstation is out there. From a feature and quality standpoint, Audacity is at the bottom of the list in almost every way. You have exceeded the level of your tools, man! Upgrade! The learning curve isn't that steep, but it is well worth it when you're done.
Someday we'll win this thing...