Not been to Papa Stour myself, only mainland Shetland, but looking at the map there's a road, small airfield and a ferry but not much else on the island.
It's also a fare drive to Lerwick for your shopping & fuel and make sure you get a good generator for the house!
If you've not lived on one of the outer islands before then I would advise spending two weeks to a month on the islands before commiting to moving up there lock, stock - just to make sure you're doing the right thing. It's a long way to go only to find you've made a mistake!
Livestock wise, there are more cattle & horses on mainland Shetland that we have here on the Western Isles but that seems about it apart from the sheep.
All the best with what ever you choose. :D
