I think there are two approaches:
- Rolling distribution
- Release distribution
I personally prefer rolling distros, since there is no such thing as upgrade to a newer version (which either way might be risky). That's why I prefer Gentoo for my servers. Unfortunately setting up gentoo requires a bit more effort, yet thanks to portage system maintaince (if you use the stable branch) is really easy and painless. The very cool feature is slots and ability do downgrade to literally any old version of the package with one simple command. On the other hand gentoo packages, even in the stable branch tend to be much newer than Debian (see point 2) - if you need a machine with recent software gentoo is for you.
Release distro - I'd choose Debian here, mainly for it's popularity around all the hosting companies and a huge packet base. Although I don't use it myself it seems to be the most reasonable distribution with a really high security level. Deployment is fast, no need to compile packages (unless you really need to).