FCC-related stress aside, Ani is political without being dogmatic, she's funky without blaring, she's poetic without being Too Too Much. My favorite studio Ani CD would probably be Out of Range (more acoustic) or Not A Pretty Girl (more electric), but the live 2-CD set is a fabulous introduction. It's called Living in Clip.
Update: 1999 brought us two new Ani CD's. First came Up Up Up Up Up Up, which is a fabulous record title. (Just say it aloud once. Humor me. There, fun, no?) And then late in the year, we got To the Teeth, which has a lot of longer-than-average songs with a lot of jammin' at the end. If you prefer less jammin' and more singin', of the two I'd go with Up x6. If you like neither jammin' nor singin', you could also get her second collaboration with Utah Phillips, which is known to the world as Fellow Workers. It's spoken-word-backed-with-tunes.
You can check out an official-looking but not-actually-official website at anidifranco.org. It's pretty impressive!
You can also garner info from online record store CDNow, but it's probably
better to support your local, non-chain-owned record store with your
purchases!