Hello. I would get a GTX770 (EVGA is my brand of choice for there great community, support, and transferable warranty -good for resale). Its $9.00 over budget but you get a free back plate and Splinter Cell blacklist for free. Also comes with a ACX cooler.
EVGA part# 02G-P4-2773-KR
Or what I did was I got a used GTX680 (reference card) used for $300.00. I got it used to to SLI my system. =)
BTW: I play at 2560x1440 and I've never hit the VRAM limit at 2gigs on my GTX680's.
If you have more then 2gigs of VRAM it may go over but that doesn't mean you loose performance. If you plan on getting a 2560x1440 or above or surrond gaming then get as much VRAM as possible to "future proof" your cards.
By the time a 1080p monitor bottlenecks because of VRAM you will prolly be looking for a new card anyways. But thats my assumptions and have no hard facts. =)
I'm just talking about personal experience with the games I play. I don't play with Mods but I do like to play on Ultra settings.
Hope that helps!~
Sidenote: I'm not here to start a war about how much VRAM is needed. If it was me, I would prolly get the 4gig version. But that's over his budget....even though I "feel" its a gimmick.