I personally use Nvidia products because their software is of better quality and hardware, when cooled properly, has longer life spans or so I have been told. They are more expensive yes, but in my mind it is worth it. Having an AMD processor shouldn't cause you any problems. Lonesome is correct in that far more games are optimized for Nvidia than Radeon cards at the moment, dying light for example.
If you are looking to pick something up there are a bunch of cheap 970's flooding the market atm. The 970's were advertised as having 4gbs of memory however because of a problem with the architecture they can only access 3.5gbs of that memory, Nvidia has issued apologies and many sellers have offered refunds to a bunch of people and a lot of sellers have refurbished cards available.
If you are looking for something less expensive the price of the 770s has gone down as they are no longer in production, still a kick ass card though I have one myself and would definitely recommend it, though it only has 2gb and won't be as "future proof".
Also EVGA all the way! Great aftermarket coolers which keep my 770 at 64c max but usually closer to 55 c. Make sure whatever you do buy something with an after market cooler pre attached and don't try and put one on a reference card yourself, you are asking for a world of invalidated warranties and trouble.
