On the performance front, especially considering hardware is tight, there is much to be gained from building apache, php and even mysql
During this process you get to choose exactly what goes in to your server, rather than ready-built binary packages that were designed to support as much as possible, but ultimately come with more overhead. No YUMming or apt-getting php-gd for Moodle, and equally php doesn't need to be built with firebird
Custom compiles allow you to ensure for instance that apache is not built with a load of unnecessary modules, or 2.2 can be build with the newly enhanced MPM threading modal, etc, which is why many web hosts opt for this.
The easiest way to go about this IMO
is with a source-based distribution; plus OS's like BSD and Gentoo lend themselves far more readily to general performance tweaking. When building the Linux kernel, for instance, you can choose to enable certain low-level file passthru streaming options that apache can take advantage of, or remove the performance overhead of, e.g. SELinux.
However getting the "perfect" moodle server could become a very involved process; nevertheless you'll learn a lot in the process
, the reward is a powerful server with an uptime measured in years, and what you can do is no longer limited by the number of checkboxes in the Red Hat control center.
Compared to the other distros that have been suggested, this is by no means the "easy" option, but if you want results then Gentoo is a good choice for the reasonably adventurous.
To clarify: The GNU is basically a developer organisation, not (yet) a piece of software!