HDTV Graphics card question

Hello today I am wondering about what kind of of system more specifically GPU configuration to display battlefield 3 on an HDTV at great resolution such as 1920x1080. I am planning on buying a 1600$ gaming rig from cyberpowerpc with these specs:
Tower:
CPU:i7 2600k O'clocked by 10%
RAM 2x4gb)8gigs of corsair vengence
GPU: I am planning on getting 600 future series from nvidia, but if i were to buy it now, i would with GTX 570 maybe GTX 580 if i can afford it so i guess the hypothetically GTX670 would prob be it. i will eventually add an SLI config for the unit in the future but for now i will be running it on one card.
PSU:1200w PSU possibly 1000w at least
Sound Card: Soundblaster Audigy 30$ card nothing high end.(dont care to much the mobo comes with decent integrated sound). Also using 100$ speakers not sure of model number.
Motherboard:GigaByte GA-Z68A-D3H-B3 Intel Z68 Chipset DDR3 ATX MB w/ Lucid Virtu + Intel Smart Response Technology & 7.1 Dolby Home Theater Audio, GbLAN, USB3.0, 2x SATA-III RAID, 2 Gen2 PCIe, 3 PCIe X1 & 2 PCI
Display:
Westinghouse 40" Class LED-LCD 1080p 120Hz HDTV, (1.5" ultra-slim) LD-4070Z
(May go with alienware optx and just watch tv on that. But for now i need to know if this system can run it on that HDTV)
I am also looking for smooth performance at these resolutions not intense lag.