Help with RAM on video cards

I'm derping pretty hard at the moment. I've been looking for a good graphics card with a good clock speed and have found one...

http://us.ncix.com/products/?sku=73018&vpn=HD7770-DC-1G...

This is just the card, I'll probably buy it from newegg. I want to run two monitors, but only use one for gaming and the other for having a stream open or something like that. Is 1GB RAM enough to power both displays? or should i try to find a card with 2gb of ram, but a slower clock speed?