How much money should I be spending to play modern games at 1080?

I want to be able to run games that came out in the last 2 years at 1080. I don't need to be on max settings although I certainly wouldn't mind being on max settings. 60fps would be nice but I don't need 60fps, I don't play competitive multiplayer games I am mostly a single player gamer. My current PC unfortunately just absolutely CANNOT keep up anymore. So I'm trying to figure out what my rough budget needs to be so I can set money aside over the next few months.