This is my first exposure to Vonnegut and I'm impressed with the amount of world building he managed to capture within a few pages depicting a single room. The heady moral questions, the implied culture and government, the emotional actions that the situation drives the characters to.
I would suggest Cat's Cradle and Slaughterhouse Five before reading Breakfast of Champions. Vonnegut uses some of the same characters across multiple books and BoC is richer if you know them already.
It's very punchy and effective stuff.
So where should I read next?