not really, a 5770 or a GTX 460 will do just fine.
the 5770 wont take any adapters at all to get a desired video output unless your using analog (VGA) but a 460 has a better performance by a slight margin

Nah, the higher the resolution, the more you'll need to spend on your graphics card if you want to play at the highest settings.

so at a lower resolution better graphics cards will play at higher settings for longer ??

Theoretically, yes. Buying an uber expensive card and then playing on a tiny 17" screen will get you crazy sky high framerates.