I feel compelled to reply now, so here goes.
The thing about Zappa is that his output is extremely varied, so it's hard to know what to recommend. If you don't like a particular song or album it's easy to assume that all Zappa is like that, which is fatal because no matter what you're listening to that's not true.
There are a number of compilation albums designed to ease people into Zappa's music. Strictly Commercial, for example, is a basic sort of greatest hits album with some of his most famous songs. The variety of the material makes it a little incohorent, but even so it does include some essential Zappa material so it's a good starting point. Other compilations worth mentioning are Strictly Genteel, an introduction to Zappa's classical music, Cheap Thrills and it's follow-up, Son of Cheap Thrills. The six volumes in the You Can't Do That On Stage Anymore series can also be a good place to start if you want a bit of an overlook.
The early albums by the original The Mothers of Invention are generally harder to get into, but if you liked We're Only In It For the Money, they might be worth checking out. Try Freak Out! (1966), Zappa's debut album, Lumpy Gravy (1968) and maybe Uncle Meat (1969). You might want to stay away from Absolutely Free (1967) and Weasels Ripped My Flesh (1970) though, if you're not adequately prepared they're hard to digest.
The album I'd recommend from the sixties though is Hot Rats (1969). It's one of Zappa's most well-known and influental albums, it contains some of his best music and it's not as weird as the earlier stuff.
Just Another Band From LA (1972) is another good example of Zappa's style, especially the way he constructed his live performances.
The mid-seventies albums are among the most popular and also among the best (IMO). Over-Nite Sensation (1973) was his first commercially successful album, and a good one for beginners. The follow-up Apostrophe (') (1974) comes from the same recording sessions and is similar in style. Roxy and Elsewhere (1974) and One Size Fits All (1975) continue in the same vein, although with a jazzier approach. A lot of memorable songs come from this era and it's probably my own favourite one. Well worth looking into.
Sheik Yerbouti (1979) is one of the heaviest Zappa albums and the best-selling one to date, so for metal fans it might be a good place to start.
I am less familiar with eighties and nineties Zappa since I haven't explored it as thoroughly yet, something I intend to do soon. By now, Zappa's classical music started to get attention so the output is more focused on orchestral recordings than previously. He also started making electronic music using the synclavier, in favour of recording with a band (although he didn't stop touring completely, the time spent on the road decreased considerably).
After his death in 1993, a lot of old and new recordings have been released. I haven't heard a lot of them myself but my impression is that they're mainly of interest to Zappa fans.
If you want to download a couple of songs, the stuff on Strictly Commercial is generally good. Peaches En Regalia and Brown Shoes Don't Make It are essential and representative of Zappa's style in their respective ways. For a taste of Zappa's guitar playing, try Muffin Man and Black Napkins. Don't Eat the Yellow Snow, Dancin' Fool, Bobby Brown Goes Down and Valley Girl are some of his biggest hits, so they might be worth getting. I'm the Slime, Montana, Cheepnis, Inca Roads and The Torture Never Stops are typical of his mid-seventies albums. You could go on like this forever...
I hope this was helpful in some way. If you want a different opinion, ask SMX who is the other big Zappa fan around here.
Finally, if you need any discography information or lyrics,
http://www.globalia.net/donlope/fz/ is the place to go.
