You could also begin with '2BR02B'. This story is set in a future world where overpopulation has led to some very strange and disturbing solutions. It's a great example of Vonnegut's ability to create thought - provoking scenarios and make the reader question the direction society might be heading. The story is not too long, so it's accessible for new readers of Vonnegut's work.
Another option is 'Welcome to the Monkey House'. This collection of short stories has a bit of everything that Vonnegut is known for. It includes his unique brand of humor, his exploration of complex social and moral issues, and his interesting characterizations. Reading this collection can give you a broad overview of what to expect from his other short stories.
A good one to start with is 'Harrison Bergeron'. It's a relatively short and very impactful story that gives a great taste of Vonnegut's style. It shows his use of satire to comment on equality in a dystopian society where everyone is made equal in the most extreme and absurd ways.