From my look into the matter, he enjoyed/admired-
Chopin (Only one interview says this, and I'm not sure how much I trust it.)
Cage (This also depends on the interview, and time. I'd say Cage influenced some of Zappa's thinking, but Zappa's less ART about it...)
He was probably familiar with many, many more. It seemed to be a field he was fascinated with. There are others where he only liked select works, like Schoenberg.
FC -- Where did you read about Zappa on Moondog? I'm curious.
Nono is someone I never got around to researching. His politics put me off, I guess. Heard a Nono piece on the radio that somehow reminded me of Frank. Didn't catch the title though...