Yea, League of Legends can probably hit 4K with decent frames (at least close to 60 if not above it) at maximum settings no problem. On medium settings I think Hitman should be able to reach 1440p and get you smooth frames as well. According to
this article, a GTX 680, which is an underclockdd GTX 770, can hit 31 fps on average at 1440p on high settings at 2x MSAA. So ideally at 1440p with
the right CPU, you can hit 60 fps on medium settings if you turn off AA (which becomes less and less necessary the higher your resolution gets).
However, that brings me to my second point -- in the case of Hitman, your FX-8350 is not ideal -- even overclocked to 4.5 GHz it only was able to generate a 53 fps average according to that article. That might sound impressive, but that's extra money spent on a cooler for overclocking and still won't serve you anywhere near as well as an Intel CPU at
stock clocks. AM3+ is a dead socket. In fact, this weekend I just upgraded from an FX-6300 to an i5-4690k. If you have a microcenter in your area, you can get an Intel motherboard and processor for a great price. I got an i5-4690k (usually $240 - $260) for $200, and I got a ASRock Z97 Extreme4 (usually $145) for only $100 (I don't know I got it for $100...the price on their site listed it as $145 but when I added it to my cart to pick it up in store it just dropped to $100). So yea, go Intel if possible. If you don't want to overclock, try for an i5-4570 or I think the i5-4590 is coming out.