I'm open to ideas but probably ETH you start worth
Next question: Why do you want to spend £645 on a graphics card that will get 31 mhs when 2 x RX 480/580s can get 56mhs for less than £500?
That's why I'm here - to ask questions and learn the best way forward. :-)
Ok then, theoretical question - can you run e.g. 1 x 1080Ti and 2 x RX580s in the same rig and mine different things or are there compatibility issues?
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.