I have a great deal of experience with the older versions of Fedora (the consumer Redhat distro) and slight experience with CentOS. I'm fairly certain that majority of Linux webservers out there are running some Redhat variant. I personally prefer the Debian/Ubuntu approach and stick with that.

Off the top of my head I know that all of the Mediatemple servers are running CentOS, and Digg runs Debian.

I think like SwellJoe said, if you're thinking about FreeBSD for the sake of going with FreeBSD and not really knowing why, then you don't want to be choosing FreeBSD. The same goes for Gentoo. Gentoo is a great distribution, but it's not for the mainstream plug-n-play let's-build-a-webapp! type of person. Gentoo, although featuring a pretty nice 'emerge' package management system, is going to require more work from you in the beginning to get it to a desirable state.

I guess there is no real answer to your question, Linux is fantastic in general as a web application server. Any distro with the base binary packages for a typical LAMP stack or even a (Rails|Django|Etc...)/Nginx configuration will treat you very nice until you reach the proverbial land of scalability. Once you see problems with your app, fix them. Don't worry too much about that right now. Also keep in mind that 99.99% of the time your application is going to be "distribution agnostic" so later on down the line if you decide you'd rather go with CentOS over Debian, or a BSD variant over Linux, you won't have any issue with that.

I'd focus more on writing a solid application and getting a solid product out the door on any of the distributions that were mentioned by the wise hackers here on HN, learn what you like as you go. As you learn more about the way Linux works and you configure things to suit your needs, the various unique characteristics of each will become more clear, and your "distro of choice" will become more evident.

Bottom Line: Go with CentOS or Ubuntu, and worry about these things as they become worries.