<cracks knuckles> Time for a fucking exposition.
(Dates in section headers are from my rough memory, I may be off by a year or two in places.)
Original Mothers of Invention (1965-1969)
Zappa started out as a social satirist; much like a Weird Al[sup]1[/sup] with a mean streak (but few direct song parodies). The music is primitive, and Frank's love of doo-wop[sup]2[/sup] is most evident here. It's probably not at all what you're looking for, but his debut album
Freak Out[sup]3[/sup] is worth a listen.
Flo & Eddie Mothers (1969-1971)
If you like crude sexual humor - and I do mean crude, the crudest ever put to rock music - go for this stuff. The movie 200 Motels was the centerpiece, but the live album
Just Another Band From LA is a classic - featuring the half-hour epic "Billy The Mountain"[sup]4[/sup].
Early solo works (1969-1972)
Hot Rats is an album you want. The opener, Peaches En Regalia, is Zappa's signature song. This is the album that put Zappa on the map as a lead guitarist. For a year during this time, Zappa was recovering from a serious accident: he got pushed offstage into a orchestra pit 12 feet below, landing on his head and breaking many bones. The impact pushed his voice box deeper into his throat, lowering his voice by a third. (That's a musical third - two whole steps.) While laid up in a wheelchair for a year, Zappa still put out 3 solo albums.
The 1974 band, Golden Age begins (1973-1975)
Zappa's best lineup. There are
five great albums.
Apostrophe (') and
Over-Nite Sensation are his two big hit albums, really a must-have for any kind of Zappa fan.
One Size Fits All is the album with Inca Roads, and
Roxy and Elsewhere has some really mind-blowing jazz. The live album
You Can't Do That On Stage Anymore Vol. 2: The Helsinki Concert is really the one to get... you are not ready for "RNDZL".
Lather, late 70s albums, Golden Age ends (1976-1981)
Zappa and his label, Warner Bros, had it out in the 70s. With 4 albums left on his deal, Zappa gave them a quadruple-album called Lather. The a is supposed to have an umlaut, and it's pronounced "leather". Zappa called it 4, WB called it 1, and everything broke down. Much of Zappa's late 70s albums include Lather, cut up into totally different albums by the label. However, much of this stuff is actually just average; the best can (and should) be obtained on a single album, the superb
Zappa In New York[sup]7[/sup].
A few albums from the Bozzio band[sup]5[/sup] are great, especially
Zoot Allures. That's another album heavy on great Zappa guitar playing.
Sheik Yerbouti from 1979 was a surprise hit, but around here Zappa's humor turns dark and misanthropic. He did like George Carlin did, became a bitter old man who stopped being funny because of it. Zappa's last real brush with popularity[sup]6[/sup] was the triple-album
Joe's Garage, another one you probably want. The last Golden Age album in my opinion is
Tinseltown Rebellion, which has Steve Vai on guitar.
The guitar albums
Later albums are pretty much for people who are already hardcore Zappa nuts, but you may want to check out:
Shut Up N Play Yer Guitar
Shut Up N Play Yer Guitar Some More
Son Of Shut Up N Play Yer Guitar Some More
Guitar
All these are double CDs full of nothing but Zappa guitar solos. They're taken from live songs, but Zappa often took a solo from this song and the backing from that one, and combined them. He sought out deliberately off-tempo and off-key combinations that sounded strange. A good example is "In-A-Gadda-Stravinsky": the band is playing the In-A-Gadda-Da-Vida riff (in one key and tempo), Zappa is playing a disjointed guitar solo (in a second key and tempo) and the horn section is playing Stravinsky (in a third key and tempo).
[sup]1[/sup] Weird Al is a Zappa fan; listen to his "Genius In France" for his take on Zappa. Very accurate.
[sup]2[/sup] Zappa is reputed to have owned the world's largest collection of doo-wop 45s.
[sup]3[/sup] Also the first double album in rock history.
[sup]4[/sup] And his little wooden wife.
[sup]5[/sup] Zappa fans often refer to his bands by the drummer's name, since a drummer change usually meant everyone changed.
[sup]6[/sup] I'm not counting Valley Girl, which is a great example of Zappa trashing a group he doesn't like without being especially funny.
[sup]7[/sup] Recorded the week Zappa hosted Saturday Night Live, which did not go well at all. So bad it's banned from reruns.