first of all i would suggest looking in a retail store to find the model you want first. you ALWAYS want to view the screen in person if at all possible first.
second if you are intending to game with it there is no reason for 120 or 240hz. tvs only take a 60hz input anyways and the extra frames are faked which causes lag in games (read up on this if you dont believe me). you WILL be using 60hz game mode anyways so why buy something you dont need. with that said, its getting harder and harder to find 60hz models anymore.
$700 for a 40" should be sufficient for base models of respected brands like sony, samsung and lg. you could go second tier with a toshiba, rca, vizio or other brand but parts availability could be an issue if it ever...