I managed to get skyrim to run on systems well below its minimum specs, including an HD3k-i5m, 8600GT-Pentium D (NOT Pentium Dual, but the old, P4 version), E350 APU.
Anyways, I'd go with either an AMD or nVidia card, and the 7700 looks good, though the 560Ti is also viable if you want nVidia.