It depends on a lot of things, like resolutions, in game settings, and which game.
If you like playing at huge resolutions (or multiple monitors) then it shouldn't be any sort of bottleneck. I doubt that's the case since you want everything, monitor included, to come in under $1000.
If you play a Cid Meyers Civ game, then same things, it shouldn't, since A.I. don't take their turns when you do.
The GTX 770 is basically a GTX 680 that's a little more powerful from clock speed, with a few power adjustments. Have you read the review for the 770? What games are you looking to play?
There are already a lot of threads like this one. Maybe the CPU is a bit different, or the GPU is another one, but in general they are all the same class.
As they say, there is always something that's being a bottleneck, it's whether you notice it or not that matters.