I have a i5-3570k (non overclocked, so basically the same CPU as you) and runs a 60 Hz monitor as well. I just bought a GTX 1660 ti OC and I'm quite happy with it (it is suppose to be the "future proof" card for 60 fps gaming at the moment, although there is no such thing as future proof).
It depends very much of the title of the game if you will see a bottleneck on your CPU or not. Most first-person-shooter don't really see a bottleneck on the CPU but I do see it on titles like GTA V Online and Elder Scrolls Online, where MMO traffic hits the CPU a bit harder.
With a i5-3570 + gt1660 ti OC 6 gb I see around
45-75 fps in GTA V Online
45-100 FPS in Elder Scrolls Online
(graphics on highest settings in both cases)
If you are perhaps planning to upgrade to a 1440p monitor you want to go with GTX 1660ti or equivalent. GTX 1650 is probably good enough as a buff if you stay with the current setup.
EDIT: Just realized you PSU is only 420W. GTX 1660 ti is recommended to use 450W.
You could also save a few bucks going with 1660 super instead of the ti version (if you upgrade the PSU)