I'm thinking about getting a new GPU which is the GTX 1660 Super or the GTX 1660 Ti and I know it will bottleneck a tiny bit but would there be any severe fps drops and stutters with the i5-3570 and the GTX 1660 Ti or Super?
Depends on the title, settings & resolution. Generally speaking, a 1660Super +/- will pair well enough with a 3570, but in CPU intensive titles, you'll be a little limited by the CPU.