Yep. We actually don't need your monitor's size, just the resolution you aim to be playing the game at.
Also, just checking, this isn't a laptop, right?
For 1080p (your grandfather's screen), and your budget, I'd hunt around sales looking for a 7770. Newegg has a 7770 GHz edition on sale for $120, but they don't ship outside the US, I don't believe.