I would suggest getting their first three live albums - they're all great collections songs from their first three periods. All The World's A Stage, Exit...Stage Left and A Show Of Hands are all single CDs packed to the brim with amazing songs from their first twelve albums, many of them some of their greatest hits and fan-favorites! If you like most of the songs from each album, you can seek out their respective studio releases from those periods.
After that, definitely get Different Stages, as you get the entirety of "2112" played live, some good tunes from Counterparts and Test For Echo, as well as some older hits, and a 3rd disc of an old show from the A Farewell To Kings Tour.
Actually, if you really want to sample Rush with a single purchase, I'd get this first. You get a double-disc dose of later Rush and a single-disc serving of early-to-middle Rush.
-Marc.