Vonnegut is definitely in the same camp as Adams and Pratchett. I like to think that Adams was influenced by Vonnegut in his own writing, as Sirens could easily have passed for a Douglas Adams novel if it'd had more jokes and a bit more Britishness.

One thing Adams and Vonnegut have in common is their almost nihilistic sense of cosmic absurdity and the futility of purpose. Without spoiling anything, the whole story in The Sirens of Titan turns out to be meaningless. A bit like how, in Hitchhiker's Guide to the Galaxy, we eventually realize that Earth was originally created by little white, superintelligent mice to compute, over billions of years, the meaning of life, the universe and everything. (The answer isn't... terribly useful.) It's absurd, and funny, and sad at the same time.

Vonnegut got more eccentric in his writing over time, but Sirens is actually very straightforward, and it's a masterpiece. Give it a shot. Cat's Cradle is also excellent. I never liked Slaughterhouse Five, which everyone recommends, as much.