Your GPU should last you awhile, I'd estimate a good year or 2 if all you're looking for is 60 fps...especially if you're willing to lower the resolution/detail settings on certain games in order to maintain 60 hz.
I had 570 4 gb paired with a 4c/8t Ryzen 5 and never came across a game I couldn't run on 1080 'high' settings at ~60 fps. I even used it for Oculus VR titles and it was adequate as long as I ran the games on low to medium detail settings. I'd definitely look into upgrading your CPU first as that is much older. Personally, I'd recommend going the AMD route, it gives you the most bang for your buck...you can't go wrong with something like a Ryzen 5 2600/3600 or even a $85 1600AF, paired with your current GPU.
Just don't upgrade for the sake of upgrading...if a new game comes out and you're finding your system is no longer adequate to satisfy YOUR requirements, upgrade or build a new one.