You don’t need to buy new phones or computers as long as they’re GSM phones. You might need new power supplies, or more probably just a plug adapter. You will need to replace any appliances that run on AC if the frequency is different (50 vs 60 cycles/sec). But major appliances are generally already in an apartment or house (depending on the custom in the country you’re moving to), which leaves things like toasters and microwaves which aren’t exorbitantly expensive.

Incidentally, mobile phone service fees are much lower than in the UK. In England, I pay the equivalent of USD $11/mo for unlimited texts and voice calls and 5 GB of mobile data. Coverage and call quality are better too. ISP charges are also lower and connection speeds are good, as long as you avoid the big providers, which are evil and have poor quality of service.

When doing international moves, which I’ve done several times in my life, a good starting principle is YAGNI: Ya Ain’t Gonna Need It. Bring irreplaceable personal items, clothes, maybe kitchenware. Big furniture, cars, etc: forget about those. Our first move filled up a container. Subsequent moves were increasingly small palletized LCL (less-than-container-load) in size.

The big hurdles aren’t moving stuff around. They’re getting residency, setting up bank accounts and finding decent work. I initially took a slightly less senior position, but quickly climbed the ladder to where I was before. This, despite being quite old for my line of work. In previous international moves, I worked for multinationals which handled immigration matters and moving, though it was up to me to get residency once I was there long enough.