[beagleboard] Best stable OS for Minecraft server?

If Debian worked well on your Pi, I'd stick with it on the 'Bone.

Robert C. Nelson's Debian images are very light by default, and you can
pull in whatever dependencies you need to get the system working:

http://elinux.org/BeagleBoardDebian#Debian_7_.28wheezy.29

The page is for the BeagleBoard, but the images work on all of the
Beagle family boards (and even some others).