Yes, the 7770 will work. But, the 550 ti and 6770 will also work. Personally, I think you'll be able to run the game just fine with a 6770. Also, if you can find a 5770 cheaper go for it because the 5770 and 6770 are the exact same card.
Sadly I have a rather decent computer and find Guild Wars 2 Struggles on the 550 TI. even on the lowest settings im finding amd cards more suitable for this game. the same card can handle most any other mmo maxed. youd be better off going for a 6850 - 6870 - or a 7000 series card. if you can afford one a 580 or 680 will give you a lot of headroom.