I would either use a G3258, FX-4300/6300, or X4-760K (or similar).
There are pros and cons to all of these. For example, a game that isn't well threaded (most) like Skyrim or StarCraft 2 will do best on the G3258 dual-core CPU. However, a game like Battlefield 4 in multiplayer is likely to do best on the FX-6300 since it can actually use most of that CPU's capabilities.
It would also matter what parts and at what prices you have access to.
After you decide on that, you want the best graphics card your budget allows. I'd suggest an AMD card as your relatively weaker CPU will benefit from any games that use Mantle (such as Sniper Elite III).
This budget, if it includes Windows as well, is very difficult to work with. I'll make an...