Frank Zappa, solo and with his band The Mothers (aka The Mothers of Invention) recorded and released over 60 albums. He recorded literally every live performance since the early 70's, and his basement was an archive. This is why "new" live albums are coming out more than ten years after his death. The set list changed every night, and there are several multi-disc live albums from the same tours out there with all different songs. He seems to be most commonly thought of as a writer of funny, often sexist or "dirty" songs, but that has hopefully faded in recent years since there's so much more offensive stuff out there. It was never his intention to offend, as some contend, but only to entertain. His stance, as with most artists, was that it was for people who liked that kind of thing, and if you don't, don't listen to it, but also don't complain about it or try to stop it, because obviously a lot of people do like it.
Folks who know more about his work also know that he wrote a lot of instrumental music, jazz, R&B, and neo-Classical. He was a fierce opponent of labelling and censorship of popular music, and one of his favorite examples of the idiocy of the system was that one of his instrumental jazz albums got the "Warning: Mature Lyrics and Content" label stuck on it. Someone obviously just put it on because it was a Zappa album.
He wrote music that he wanted to hear, regardless of how easy or difficult it was to actually play. He tended to surround himself with top-shelf musicians, because they were the only ones capable of playing his complex and challenging music. His music is often off the wall, considered rather boring and pointless by some, experimental and brilliant by others. I have over 40 albums (CDs, records, whatever) of his work, and some of it is brilliant, and some of it I find boring and pointless. Toward the end of his life, his health prevented him from touring (he died of cancer in the early 90's), so he composed and recorded primarly on the Synclavier, an early keyboard-computer-synthesizer capable of basically playing anything you can write. He admitted that while it was gratifying to actually hear his compositions played perfectly, he discovered that "perfect" was overrated. He preferred the interaction of playing with a live band and having his music played by actual musicians.
One recommended starting point would be his first solo album, "Hot Rats". It is mostly instrumental, with mostly "normal" instrumentation and jazzy, R&B arrangements. There is one "funny" song, and a few of the tracks get a bit experimental, but I consider the whole thing pretty good, and consistent.
Another good starter would be "Zappa/Mothers Live: Roxy & Elsewhere". Absolutely fantastic musicianship, killer horn section, and lots of funny songs. A great audience-participation track (he was also known for this part of his show) where he brings people up to try and dance to the weird stuff they play. It's funnier than it sounds.
Fans of neoClassical might try "The Yellow Shark" performed by The Ensemble Modern. It's different. I can't say I much like it, but I'll admit that the playing and arrangements are awesome. It's not my thing, but a lot of people really love it.
Electronica folks might check out "Jazz from Hell", one of his Synclavier albums. Music performed untouched by human hands. It's pretty mind-blowing. I like it, but can only handle it in small doses. A couple tracks at a time, and I feel like I need a cigarette (and I don't even smoke).
