Back when I had a 6850 @ 6870 clocks and my trusty E7300 @ 3.6 GHz (450*8, RAM 1:1), I thought I didn't have enough video card grunt for games like the assassins' creed of the time (was it brotherhood or revelations?, sure it was before AC3, memory is fuzzy right now). I regretted not buying the 6950 back then, seeing 30-40 FPS at most and a not very enjoyable experience.
Around that time I upgraded to my 2500k as I have it right now, and even at stock , suddenly the very same game with the very same 6850 ran at >60 FPS maxed out. And it continued playing every game up to last November when I upgraded to a 290, since the newer games from the PS4/XB1 generation proved too much for the little 6850. 4 nice years!
Considering the PII was quite similar to Core 2 in clock per clock comparisons and you have 4 cores in constrast to my experience with a dual core system, I'd say you could get a better graphics card but something like a 270x or 285 could be in the upper levels of what your system can handle. Cheap cards, thankfully. Still, having cards like aftermarket 290s on sale all the time (200-250 USD) that crush these two I've mentioned, they're not too tempting. You could get a powerful card and later upgrade the rest of your rig to follow suit, provided your PSU can handle the upgrade.
If you like nV, well, the 960 isn't a compelling buy in price/performance, the 970's future is dubious with its bizarre memory configuration, and the 980 is an overpriced piece of crap considering the 980TI completely destroys its for a little more, but then you're spending USD 650. Quite a stretch from a decent 290, and this card requires at least a highly clocked i5 to put it to good use. Not cheap.
By all means if you upgrade your card overclock that 955 (a BE, easy multiplier OC) to maximize your investment.