I am assuming that you are playing at a 1080p or lower resolution.
You see, games vary hugely in terms of graphics. For about 400-500 U.S. dollars,(tower only, you still need a mouse, monitor, and OS) you can create a pc that could run most fairly modern games on medium settins with about 30-40 fps. Think Skyrim, League of Legends, and maybe even Battlefield 3. But modern titles like Alien Isolation and Battlefield 4 will only be playable at very low settings.
Here is a page showing some useful build lists: http://elitegamingcomputers.com/good-cheap-gaming-computers/