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A GPU that will play anything at max settings (1080p) for 5 to 10 years will be most of your budget by itself. 

A system with an i5 and a gtx 970  will set you back around 550 just for those 2 components, unless you buy used gear. 

Unfortunately it is pretty expensive if you really want a decent gaming pc, but you would be surprised how little difference there is between max and medium settings in most games.