GTX 670m is between the desktop GTX 550 ti and GTX 560
The battery will last for 6-8 minutes
Select the 16GB RAM upgrade (it is cheap). Also select BD ROM and W7 HP 64bit. Total is $1499 (so I managed to maxed out your budget).
Select i7-2630QM, BD ROM and W7 HP 64bit and save yourself couple of hundred bucks.