Thanks guys, I was thinking about MSI GTX 1060 GAMING X PLUS and I'll go with it for now.
Maybe a silly question: would it be possible to make one rig containing both AMD and Nvidia cards at the same time? Like 3x 1060 and 3x rx580?
Yes, you can run Nvidia and AMD cards on the same rig. I just added a MSI 1080 Gaming X to my RX 480 rig. The Nvidia cards are also easier to setup, just install the latest driver and it runs out of the box. No bios patches, driver patches or hard system crashes like with the AMD drivers.