ATI has gotten a lot better with their linux drivers. Trying to get dual monitor support to work will probably cost you a few hairs, but aside from that, no worries.
NAS system: FreeNAS. Awesome distro, running it here. Supports software raid, and eats like 32 megs of ram when idling. Nice web interface, too.
Although not technically linux (it's BSD), I think it suits your needs.
As far as a full blown backup solution goes, see here:
http://www.jupiterbroadcasting.com/?p=2649
Apps are in the shownotes, and the backup section is around the end of the show I think.
As a base OS for those full backup solutions, I'd go for either CentOS (red-hat base) or Ubuntu server (Debian based). Keep in mind that Ubuntu server is full console, so no GUI whatshowever. If you want a graphical interface for the server with Ubuntu, it's best to pick Debian (Ubuntu's ancestor).