Mint 12 uses Gnome 3 which has problems with certain ATI cards, even if you use the open source drivers.
However this does seem to have been fixed with the latest drivers from AMD (11.12).
If you are going to use Gnome3 then an nvidia card is probably best for you.
However, IMHO ATI cards for me have been lot better under Gnome2, XFCE and KDE.
Don't Dream it....Be it..