Both 11.10 and 12.04 can run on that system. However...
There is a particular problem with Ubuntu 12.04's installer and some older Athlon CPUs, including the 2200+. The installer will crash at an early stage unless you run a workaround. Fortunately the workaround is pretty simple.
When you boot the Ubuntu 12.04 live CD (or USB), choose 'Try Ubuntu before you install'. It will (eventually!) boot into the Ubuntu desktop. Click on the Ubuntu icon (top left) and type 'terminal'. Click the Terminal icon that comes up. In the terminal, type:
sudo apt-get remove ubiquity-slideshow-ubuntu
and press enter. This will remove the package that causes the problem. You can then double-click on the 'Install Ubuntu 12.04 LTS' icon and you should be fine.
I should add, though, that there is another unfortunate bug associated with this range of old Athlon CPUs, and that is that Adobe's latest version of Flash for Linux at the time of writing, 11.2, is compiled in such a way that it no longer runs on these chips. I read that it is possible to install an older version (11.1 is said to work). It's a kludge, but one I am prepared to try!