FreeBSD is the one you should run. It has the best performance and hardware/software compatibility of the three. It's the easiest to get off the ground with for a beginner as well, so it's also a good starting point.

NetBSD is the one whose source you should study. The emphasis is on correctness and portability. The book Code Reading by Diomidis Spinellis used mainly examples from NetBSD even though he is a FreeBSD developer, because (he implies) the code is easier to read.

OpenBSD forked first and developed a reason to exist second; its storied past is really quite an interesting read, but won't leave you feeling like it is being developed by the greatest minds in security for exactly that purpose. I think its secure reputation is more fiat than fact and I'd like to see recent benchmarks substantiating the notion that it is better to run on routers and whatnot. I have no use for it.