Desktop to withstand frequent game use?

I'm looking for a relatively "cheap" desktop to use for mostly playing league of legends and minecraft on.
Can anyone give me any recommendations on some desktops that aren't necessarily meant for gaming, but can withstand those two games with frequent use?
My preferred price range is $200-$600
I'm not really looking for a gaming computer because those are the only two games i play but if any are in the price range that are dependable than i'd like to here about them.