GTX760 will perform fabulously in 1080p but 1600!!! Don't even think about it. For that you at least need a 780 from the Nvidia side but r9 290x will be the best.
1600p gives you a higher res which will make things look great but 1080p looks good also. In my opinion i think 1080p is better choice because the higher res monitors at a good size as just stupid in price unless you find some non namebrand cheap thing which probably wouldnt be a good idea to purchase anyway. I would get the 780 or 280x at minimum.
I'd say the 7870, but if you don't mind spending more for the 7950 you can get that instead. Because the 7950 has amazing overclocking potential that leaves the 760 behind.