The Big Two are Cat's Cradle and Slaughterhouse Five. They're the two you're mostly likely to end up talking with someone about, or to have familiarity assumed by an article or something. If we were to make it a Big Three the third one would be Breakfast of Champions.

His worst are probably Slapstick and Timequake, and the latter's so full of references to his earlier works that you wouldn't want to make it an early read regardless.

The short fiction/non-fic collections published during his lifetime are generally great. Big exception for A Man Without a Country which was pretty mediocre overall. Anything posthumous is suspect and should be deferred until you've worked through the earlier stuff, if not avoided entirely. Not that there's nothing good in there, it's just that the average quality is way lower.

Personal favorites of mine that don't generally make best-of lists are Deadeye Dick and Bluebeard. If you're reading him for the sci-fi connection rather than as general fiction, you want the Big Two plus Sirens of Titan (which would probably be #4 in a "big four" as far as importance-to-have-read) mainly.

Slaughterhouse-five - probably his most well-known work, and at least partly based on his own experiences in Dresden in World War II.

It's a very Vonnegut book, and a great gateway to the rest of his writing.

I liked the Sirens of Titan. Here, read a couple of pages: https://www.flickr.com/photos/romasita/2766136797

Slapstick was one of my favorites, plenty of sarcasm to go around. I've been trying to get through Player Piano (his first novel) but it's a tad dry.

Cat's Cradle. Not too long. Themes include science, apocalypse, and religion.