I recommend Debian Stable.  Why do I suggest Debian over other distros?
1.  Debian is more stable and reliable than other distros.
2.  Debian easier to work with.
3.  Even if you don't think Debian is inherently easier to work with than other distros, the fact remains that the larger user base makes it easier to find the help you need from discussion forums and web searches.

Why do I suggest Debian Stable over Debian Testing?
1.  Debian Stable requires much smaller and less frequent updates than Debian Testing.
2.  Debian Stable is much more stable.  You clearly indicated that you value stability over having the newest software.  (And that's a common priority for servers.)

-- 
Jason Hsu <jhsu802701 at jasonhsu.com>