If possible, try to get a Ryzen 5 1600, even if you have to go with something like an RX 580 4 GB for it. Ryzen 5 1600 will be much more future-proof for gaming. You can also mix the two - Ryzen+ GTX 1060. But I'd definitely go with the Ryzen CPU, an either of the GPU is fine. Do note that RX 580 has inflated price right now, so you'll have to wait if you want to buy it at normal prices. Otherwise, just get a GTX 1060 6 GB, it'll be just as good.
And, in case you don't know, yes you can mix an AMD motherboard with an Nvidia GPU, there are no problems there.