Most would say his most famous book is "Slaughterhouse Five." That book is widely considered one of the best American novels of the 20th Century.
One of his novels, "Breakfast of Champions" was also a best selling novel for him. He also wrote, "Welcome to the Monkey House", "God Bless You, Dr. Kevorkian", and many others.
inauthor:Kurt inauthor:Vonnegut - Google Book Search
To give you a suggestion as to where you want to start, try looking at a synopsis of each of his works and see if you what grabs your interest.
Personally, I preferred "A Man Without A Country."