No. You're fine right where you are. Audacity doesn't Save sound files. It saves Projects. Projects are collections of files -- some collections with quite a few different files -- that can be made into one good sound file or show file later on. Audacity does it this way because you can edit a very complex show with a modest, slow computer.
Anyway, just from right where you are, you can Export > WAV (Microsoft) signed 16-bit PCM. If you have Windows showing you file extensions, it will look something like ViolinRehersal.wav. If you have normal Windows, you'll get ViolinRehersal and the wrong icon. That file should play just fine in Windows Media and, of course, in Audacity.
You can use Audacity to Export an MP3, too, but Audacity is required to be missing the software to do that. You can install the "lame" software to your Audacity yourself and that will let you Export (not Save) an MP3 file.
http://audacityteam.org/download/plugins
Scroll down to the lame software. It's what passes for a joke in the programming community. It's a recursive phrase. "Lame Ain't an Mp3 Encoder." Programmers don't get out much.
If you start having serious problems getting this to work, we're probably going to send you to version 1.3.12 of Audacity instead of 1.2. Audacity 1.2 is seriously old and can have problems on newer computers.
Koz