1920 x 1080 graphics card question

I am looking at spending between $2,000 and $2,200 sometime next year to build my first gaming computer. I have decided that I will go with 16 GB of RAM and whatever replaces the current top-end overclock-able Intel i5 or the AMD FX-8350 (if it shows significant improvement over the 8150 or results similar to the i5). I am looking at a video card that can handle 1920 x 1080 graphics at high or max resolution settings with as little lag and stuttering as possible. Although I don't play games such as Call of Duty or Battlefield, I have played other first person shooter games and jet or space fighter games in the past and would like to have those graphics capabilities if there is one that catches my attention. From my research I am guessing the cost would be somewhere in the $400 range. If you could provide me a more realistic estimate on the price or information about a card capable of meeting the specs that I am looking for at a lower price, I would appreciate it.