You will need a new platform to upgrade. The FX socket is dead. But a modern CPU will offer a substantial boost to performance. Unfortunately, a new platform will be expensive as you will need a new CPU/Mobo/RAM.
I would not get anything slower than the i7 2600 or i7 3770.
I'd try to avoid ones like i7 860 or 870 these days.
But like the system above, you could probably pick up a box like that, add the ram from your system, change the power supply with your current one. Hopefully your gtx 1060 would fit it.
Maybe for another 15 bucks get 4gb of ram more to make it an even 16gb, and grab an SSD. You can get a 240gb for about 30 bucks these days. I think even that old i7 with your 1060, that would easy the FX CPU for lunch.
Will that i7 2600 be the fastest cpu? Of course not, but if you look up benchmarks on YouTube for example, it holds it's open against an i3 8100. It may not have as many fps at times but I notice when watching some of the clips it's not as heavily loaded as the newer i3 due to the hyper threading.
So in other words, if you can wait, ryzen. If you most so something now, then an older used/refurbished PC from an office with an i7 is probably a decent option I would think.