Dang with that budget I would personally go with:
http://www.newegg.com/Product/Produc...82E16834152590
$1,599
Ghost series so it's in the thin and light category. Plus it has the 870M gpu:
http://www.notebookcheck.net/NVIDIA-....107792.0.html
Scroll to the bottom, shows frame rates of 35 on ultra for Metro: Last Night, which is pretty good for a laptop card.
Or I would go,
http://www.newegg.com/Product/Produc...82E16834152686
Which is $1,899 but has 16 GB RAM, instead of 12, but as others have said unless you are doing a lot of multi-tasking isn't a huge deal. Also has the 970M. It is also the ghost series (I am particular to the thin and light designs). The 970M runs Metro: Last Night at 53 FPS on ultra, which is damn nice for a laptop card.
Didn't know you had such a decent budget or I wouldn't have even thrown out my lenovo suggestions lol.