The books do have some mature themes and quite a bit of swearing. I did put them in chronological order, so you could read them that way. The Fault in Our Stars (TFiOS) is the one everyone's talking about, since the movie's coming out in June. Paper Towns has less (maybe none, I can't recall) mature content. He also has a few collab books with other authors and such, like Will Grayson, Will Grayson. Haven't read An Abundance of Katherines, so can't call judgement on that. But they're all fantastic books.
I personally started with Paper Towns, because that was the most available, then Looking for Alaska and Will Grayson Will Grayson, followed by TFiOS.