The resolution you're gaming as is just a tad higher than 720p - not much horsepower these days is required to drive 60FPS at high/ultra settings at 720p, the only real thing to consider is frame buffer (amount of dedicated VRAM) used in postprocessing and anti-aliasing.
an R9 370 (AMD's cheapest gaming oriented card) will drive good frame rates at 720p on high settings, and won't break the bank - but it's frame buffer of 2GB is a bit limiting.
As was previously said, NVIDIA do seem to be friendlier towards TV-type screens compared to AMD cards - Though either will work, AMD just tend to have this flicker (mostly due to the type of input mechanism used in TVs) that can get a bit annoying.
Cards I'd recommend for you (Also as previously stated, you'll need a good quality power unit from a company such as SeaSonic, Corsair, Cooler Master or EVGA... Most power units are MADE by SeaSonic and then rebranded by other manufacturers
GTX 960/970 - 960 is way powerful enough to drive high/ultra gaming with reasonable MSAA at 720p... 970 is overkill but you can push more post-processing and crank everything up that bit more and not have to worry about frame rates, it also has double the frame buffer of the 960 (4GB).
AMD R9 380/390 - 4GBs and 8GBs respectively, you might run into some flickering or other annoying issues with AMD as I said before, but you can't deny the horsepower or the VRAM on offer here for this price. Bare in mind, AMD cards have a higher thermal design profile and will probably run hotter and use more power.