Usually, when you sell your secondhand UK stuff (on Ebay, local paper, whatever) you get a load of hassle, and not much money. And then you come over here and buy brand new stuff at full retail price. So it does not seem very efficient! :-) But it's certainly a lot less aggravation to dump your stuff and buy new as required.
I voted for that option ('cos I'm lazy), but my Mrs. was very attached to the leather sofa, and some almost brand-new appliances (washing machine, fridge/freezer, smart TVs) so she insisted we bring them. I had to pay a man-and-a-van (a Luton). They're a lot cheaper than a full-service removal company, but not sure how many such folks are still doing international deals post Brexit. Cost me 1,500 quid or so a few years ago, so even if you could find one, it will be much more. (And I probably got a good deal, as he already had booked a job bringing stuff back from Bulgaria for a lady returning to UK.)
So I guess if you've got some valuable stuff it might pay. We didn't have much, but maybe a couple of grand new. Plus we squeezed my bikes and my motorcycle in. That's another couple of grand... and I'm pretty sure I would have just about died trying to ride my motorcycle 2,000 miles. So that made me feel better about the deal. :-) And you can squeeze in a bunch of suitcases and boxes of whatever you've got. Oh... and as the motorcycle was in the van, and the vanman shared the driving with his son, I decided to drive my trusty old diesel Vectra over, in convoy. I could have got 500 quid for it in the UK, and then spent a few grand getting a Bulgarian replacement. As it's still going strong 5 years later, I'm quite pleased with that aspect of the deal (plus I loaded the Vectra up with a trailer and a ton of stuff too).
But... our house renovation wasn't finished... so there wasn't much room for our stuff anyway. I've enjoyed the bikes and the motorcycle over here, but apart from that, everything's still piled up in the basement (and the trailer), and the only appliance we dug out was the microwave. :-)
One of our expat member recently did it himself. as he couldn't find a man-with-a-man to do it. He bought a cheap and cheerful long wheelbase Transit on Ebay, and loaded everything up in that. Must have been a few grand for the van, and a good chunk for fuel, vignettes, food, accommodation driving over. Their property agent accepted the van as his commission.
As to prices, appliances are pretty much the same as anywhere else. You can compare on Technopolis or Praktiker or Technomarket (all dot-bg)