I've had my PC for many years now and I can't seem to run new games at a smooth frame rate and decent graphics/visuals. I don't have an unlimited budget but I am looking for something that will last.

Current Specs; as displayed on Computer as I don't know much about PC's

Intel(R) Core(TM) i7-3370 CPU @ 3.40GHz 3.40GHz. / 8GB of RAM. / NVIDIA GeForce GTX 660.

Goal: I want to be able to run modern multi-player games like at a smooth 60+ FPS whiling running NVIDIA Shadowplay and decent in-game graphic settings.

P.S I've recently decided to make the full time switch to PC as a gaming platform so I really want to upgrade to something that will keep me going for awhile.