I don't have exactly the experience you're about to have, but some similar, so will share what might be useful.
Moving regular farm equipment probably not cost effective. Should be able to sell existing and buy replacements for similar amounts.
On-site Farm dispersal sales are the same everywhere - some items will go for way more than they're worth, that's the neighbours giving the outgoing family a good sendoff, so do your homework before you bid! But if you make yourself known to the auctioneer as the incoming farmer, everyone will get to know that, and the locals are unlikely to bid you up over the odds for essential equipment.
Moving livestock, I'd say, unless you have cherished bloodlines, you'll make more friends selling up and buying new. Not only will you make lots of good contacts buying, but it will be appreciated you not bringing potential problems (You'll be moving to TB free, from TB endemic, for instance.) The reverse also applies, your Welsh livestock would be meeting diseases they've no resistance to. (Tick borne diseases are renown for being very regional, for instance.)
You may find a farm you can buy complete with livestock, we did that in Northumberland and it was a great help. The sheep all knew what to do, and that helped while we were learning our new ground! lol. The outgoing farmer let us come and work a few gathers and work days with him too, and handed over his medicines book and so on, which gave us such a good start.
Until I moved to Northumberland and Cumbria, I was of the type who'd say, "No such thing as bad weather, just inappropriate clothing."
Well, that was a no-nothing southerner for you (despite my experience living on Exmoor, which is a fairly harsh environment... Harsher than West Wales, I think.)
Living and working with the northern weather shapes everything you buy, everything you do, everything you eat. Do not underestimate what a learning curve - and culture shock - it will be!
I haven't farmed on Orkney but I did a farmers' touring holiday - touring farms! - for a week up there, so got a few insights. (Any actual locals can tell us if I have this right!)
Everything needs housing and all shutters battened down all winter, the winds are horizontal, but all the cattle grow like topsy on the good ground when they can be out. Not much of a market for sheep, though; the situation re an abattoir on Orkney is an ongoing saga; livestock transport to and from the mainland exists but may be pricey to use.
No foxes on Orkney, and precious few trees!