Like many have already said, the distro to choose is probably the one you're most comfortable with. All major distros contain much the same core software, most differences are relatively superficial on a server with no GUI.

Anyone running a real world server is going to need general Linux skills regardless of distro, no magic tools fix everything all the time. Community support is an important consideration, more or less in inverse proportion to your Linux admin skills.

Personally, I prefer Slackware for servers but I couldn't recommend it to someone without fairly well developed Linux command line skills. With Slackware, I find it easy to build a lean, mean, robust and secure server that only runs what is absolutely necessary.

For clients that need/want to do some of their own system administration using GUI tools, I have used Fedora 3 without any problems. Moodle requires a fairly standard and well understood LAMP environment and not much more, so I don't see Fedora's stability as a major issue.

Again, Linux is Linux is Linux, no distro provides an automatic guarantee of problem-free sysadministration.