Videoram alone isn't the answer. I currently game on 1920x1080 with a 4870 512mb card, and am very happy with it (though I do miss my x2). Highspeed video ram combined with a good GPU is the answer for large resolutions. A 1gb GDDR2 9500gt for example, would be a waste, as the card can't even use the ram (its a marketting gimmick) but makes better use of 1gb on the DDR3 version.
Gaming without AA/AF will reduce your needs heartily, as those functions are resource hogs. You might get by with the 9600GT, but would probably be better served by at least an Nvidia 250 or ATI 4850.
Notice BSD, that he didn't mention details, just the resolution. If you want higher details running at that resolution, indeed, your should set your minimum sights at the 260 or 4870. In those cards, extra ram works well (though not essential without AA/AF or ultra high details).