Your CPU is going to be a bottleneck for any modern graphics card (It's 10+ years old). Also, there is no reason to get the RX 480 over the 1060 as the 1060 is actually cheaper and faster.
The x4 860k came out in 2014...
OP, I would go no higher than the 1060/RX480, as your CPU will hold back performance of these and anything faster.