In that price range look for the Lenovo Ideapads, like the 410p or the 510p, if you dont want to reach the top end of your budget then you can just get the more basic variation of the 410p series which go from $720 to $750, also look for coupons as Lenovo always has some sort of sale going on on their website
Even the basic models should be enough for med to high level gaming (depending on application)