770, 7970, or r9 280x?

R9 280X

Not if you overclock the FX6300, any card really they are all in the same performance group so really I would take price into consideration and call the 280X and GTX770 equal and 7970 a little less power.

More info regarding your system is required for a decent answer. What resolution will you be using? (this has an important bearing on how much vram you need) Psu size? Are free games an important consideration for you? (depending on your area, you might get 1 or more free games with certain cards).

Go for the GTX 770. I have one and it's awesome, and you can get them for around $330 to $340 now. It's slightly more powerful than an R9 280X in most cases, though it does but heads with it in others. However, Nvidia does have much better drivers and that'll mean SLI is a good possibility in future.

However, I also have an FX-6300 and I can guarantee that for some games you will bottleneck. Such games include Crysis 1 (frequently, mostly about 30 fps average), Skyrim (infrequently, almost always 60 fps), and Borderlands 2 (somewhat infrequently, most of the time 60 fps). But I guarantee you there will be bottlenecking, absolutely no question about it. I've overclocked to a very stable 4.2 GHz and there's still bottlenecking, but again, it's game dependent and every game is still extremely playable.

UPDATE: Seriously, people have to stop saying "Oh, overclock and you're fine". That's not how it works. It has a lot to do with optimization and how developers take advantage of logical cores (AMD uses logical cores which suck and aren't actually real cores) compared to how they take advantage of physical cores (Intel uses physical cores, which are real cores, which is why 4 Intel cores = 8 AMD cores). But overclocking can help somewhat, though not as much as you'd hope.

A good 4.2 GHz OC like my own can give you anywhere from 4 - 8 more fps on your minimum frame rate which could be fantastic, or it could mean relatively little overall depending on how bad your minimum is. For example, in Borderlands 2 my minimum in a certain area was like 38 fps (which looks awful on that game, by the way, due to lack of motion blur) but it was relatively infrequent and only occurred in a few areas. After I overclocked my minimum for that area was now 44 fps, which was a good increase, but it still felt lacking overall, and it didn't help that later on I encountered another area which dropped me to 30 fps.

Point is, overclocking with a budget CPU isn't going to make it into a higher end CPU. It'll help, but nowhere near as much as people will say it does. Bottlenecking will still be extremely prevalent, and you'll notice it in CPU bound games, and it's simply a matter of training yourself to deal with it. You'll be much happier overall if you can learn to just accept your bottlenecking rather than constantly stressing over it.

Well I personally would not pair a a $300 GPU with anything less than an I5 or FX83xx at 4Ghz but that is not what people want to hear here. FX6300 is fine with the $200 class or 270X HD7870 GTX660. I call it balance. either you are building a budget rig or high end.