How much GPU do I really need for 2 screens?

I'm ordering parts this week, and would like the opinions of the experienced collective here. My goals for this machine: Gaming, specifically I play a lot of WoW and Eve Online (neither of which are graphic intensive by modern cards standards, I know). I plan on playing Elder Scrolls Online when it is released. As far as non MMORPGs, I would like to play Metro 2033: Last Light, Borderlands 2, Skyrim (modded heavily), GTA 5, Star Citizen (who knows when that will come out, so it probably doesn't factor in), and Sim City without having to step down the graphics options. I will be using 2 1080 monitors, although the second one is going to be for desktop stuff to avoid tabbing out. I'm thinking GTX 670 2GB is the right card, but I don't know if it is for sure, or if I should get cheaper one and still be able to do what I want (or do I need a 680, or should I go AMD?)

Here's what I'm ordering if the 670 is satisfactory for this (hopefully the link works)

http://pcpartpicker.com/p/D2yv

In case the link didn't work, here's a list of the parts that will matter as far as bottlenecking performance

CPU - i5 3570K

Cooler - NH-D14

Buying some Artic Silver compound, as I don't know what comes with those

Motherboard - Asus P8Z77-V LE Plus

Memory - 8GB G-skill 1600 (CAS 7)

SSD - Samsung 840 Pro 256 GB

GPU - GTX 670 (or if there is a better suggestion?)

Monitors - Samsung S24B350HL x2


As an aside note, I figured a HAF-X case would do the trick and looks nice, but if anyone suggests a nice looking case with good airflow, I'm open to suggestions

Thanks in advance