Yeah, the GTX 770 (Heavily overclocked GTX 680 rebadge) would be a very good choice for 1080p. As to Vram amount, 2GB is fine, but if your playing a heavily modded Skyrim for example, it can help . My GTX 670 2GB was running out of Vram with the 78 mods i have ATM, and as a result iv'e had too decrease my game settings a little to compensate.
The AMD equivalent would be the R9 280X (AMD 7970 rebadge), but for some reason in the USA at least, they are priced much higher than a GTX 770 2GB & almost equally or still more than a GTX 770 4GB. Which is odd considering they perform similarly, with the usual game to game favoring of one or the other. And it's Ironic that the 280X released cheaper than the GTX 770 as well, lol.
i5-760 2.8Ghz/Asus P7P55D-E / Titan Fenrir EVO/Kingston 4GB
2xWD C.Black 640GB (RAID 0)/Gainward GTX 670 Phantom/Corsair TX850w
Sound Blaster Z /CM 310/W7 HP 64bit/Asus PB278Q 2560x1440p
Zowie AM-GS/Filco Maj.2 (mx brown)/Senn.PC360/Corsair SP2500
Self built PC problems Here
Can i run game XYZ Here
How do PSU's work Here
Whats in your PC Here
Keep your PC clean Here
How to build a PC Here & Here