I have about 1300 dollars to spend on a gaming computer. I am a web designer and I play alot of games. Such as League of Legends and WoW. I want to focus on FPS and Graphics. I normally listen to spotify, play League, and listen to my friends on skype. I would like about 16G of ram and a high quality video card.
I was building something similar (maybe a few hundred more).
I'd get a Intel Core i5-4670K processor (~$200), Gskill Ares 2x8GB 1866 RAM (~$130) and a nVidia 770 ($330 after price drop) which you can always SLI later. If you can shell out a bit more, get a 780 for $500. Either way, you'll get Batman Arkham Origins and Assassins Creed IV for free.
Upgrade PSU. That build can handle most games in 1080p at 60hz (is your TV 60hz or 120hz?), maybe can't max battlefield 4 or recent AAA titles without OC. If you turn of AA, it will handle everything that comes out in a next few months.