I'm relatively new at this and I've looked at custom PC builders but even I know they're way overpriced.
The main purpose of this computer is to be able to run the most recent blockbuster games as well as the ones in the near future. I would hope to be able to run Battlefield 4 pretty smoothly (if not on the best settings).
If the $1200 - $1500 budget is not enough, the max I'd go up to is $1700.
Here you go, this will absolutely hammer anything at 1080p. The 780 will allow you to play BF4 with ultra settings (everything maxed except for the resolution scale) at 60fps on any size map. Also the RAM is only 1600Mhz but it is a CAS latency of 7 which will be faster than 1866C9. You could also drop the 1TB HDD and upgrade to a 250GB SSD if you don't think you will need that large of a storage drive. Also the case is pretty much up to you, although I suggested a super solid one that fits your budget nicely.