Zappa's discography can be...overwhelming since he has a crazy number of albums. (I might be able to make more suggestions later when I get on my laptop)

My dad got me Apostrophe one year for Christmas and I have loved him ever since so I'd suggest starting there as I think it is a great example of 70's Zappa.
If you like that I also suggest Hot Rats, Sheik Yerbouti, and Joe's Garage. Probably in that order.

Early Frank Zappa and the Mothers of Invention has a different sound but I like it a lot (maybe more? hard to say) than Zappa's later stuff. Freak Out! And We're Only in it for the Money are both great albums.

If you'd like a compilation album to sort of test a few things, Strictly Commerical is a nice sampling of his stuff.  And finally If you like his music I also suggest his autobiography, its funny, and weird, and great. And you get to learn the crazy story of how his voice dropped like an octave.