Quite hard to answer that.
In a lot of book shops you will find him under Science Fiction, in the better bookshops you won't.
As he said himself
I have been a soreheaded occupant of a file drawer labeled "Science Fiction" and I would like out, particularly since so many serious critics regularly mistake the drawer for a urinal.
SlaughterHouse 5 for instance opens with the Hero 'Billy Pilgrim' as an American GI captured by the Germans in WW2 and held overnight in a basement in Dresden. That night the Allies firebomb Dresden killing a lot of civilians and destroying lots of porcelein factories.
Pilgrim survives and is bought out of his safe basement to see the devastation and the dead, he is convinced the Germans are going to shoot the allied prisoners.
(So far this us exactly what happened to Vonnegut as a young man!)
Then he gets abducted by Aliens and finds himself an exhibit in a zoo on the planet Tralfamadore, where he is expected to have sex three times a day with the other occupant of his cage.
So which part of the storey is more insane?
His books parody life in so many ways, the early stuff like Player Piano was written in the 50's and parodies Roosevelts New Deal, he wrote from the fifties until a few years ago, he came out of retirement to write a scathing attack on George Dubya which has yet to be published in the UK (not sure about the USA)
He had a son who was wrongly diagnosed and wrongly medicated as a Schitzophrenic, some of his comments about mental health and sanity are thought provoking and often very funny.
Vonnegut at his best tilts at all the accepted windmills of society, he pokes fun, makes you think and makes you laugh.
Some of his stuff may seem out of date, as it was written of it's time, quite often he uses other planets and time travel as settings for his imaginary societies and perhaps this is where the 'Sciece Fiction' label came from.
'Kilgore Trout' (who I mentioned in a previous post) is a character who turns up a lot in Vonnegut books, he is an author who has trouble getting his science fiction books published, so they get published as 'pulp fiction' with erotic titles and covers and are sold in Porn Shops, on the basis that when the punter gets the book home and discovers it is not a wank book he will be too embarrassed to take it back.
Vonnegut published a book called 'Venus on the half Shell' in the name of Kilgore Trout. It found it's way into bookshops, and was often put in Science Fiction under 'T'
Start with Slaughterhouse 5 it is as good a place as any, and the one book of his that is on School recommended fiction lists these days, and they made a film of it