You should definitely use FindBugs. In my experience, the false-positive rate is very low, and even the least-critical warnings it reports are worth addressing to some extent.
As for Checkstyle vs. PMD, I would not use Checkstyle since it is pretty much only concerned with style. In my experience, Checkstyle will report on a ton of things that are completely irrelevant. PMD on the other hand is also able to point out questionable coding practices and its output is generally more relevant and useful.