I've left the US three times to live elsewhere, the shortest of the three stays abroad was five years.
Mailing address: agreed. But a PO box won't work for some things, so find someone you can trust who'll let you send mail to their address.
Bank accounts are tricky to establish quickly, but you won't be able to do a lot of basic things like get utilities turned on or rent a flat without a local bank account. Even then, your credit rating's going to suck for a while.
Don't bring anything except irreplaceable items with sentimental value. Computers will generally work OK. I'd never think of bringing a car. Sell it. Sell everything you can. Give what you can't sell away. Storage costs are a drain. Extra cash is more helpful.
Expect hassles and absurd expense getting car insurance since you won't have a driving record in your new host country. At some point, you'll need a host-country driver's license and that can also be a pain in the ass. But on one occasion, I lived in a big city with good transit and didn't need a car for the first 6 years of my stay.
Similarly, many countries are parochial about qualifications and work experience, and don't have a clue about your education or experience in the US and whether you're lying about it or not. You'll have to prove yourself all over again.
Arrange accommodation at your new place before your shipment is scheduled to arrive. Shipping can take a few weeks. We did an LCL (less than container load) palletized move. We got a freight expediter to palletize it and to handle all the paperwork. It wasn't crazy expensive, 3/4 of a ton of stuff was about $400. I knew someone who knew someone in the business, that helped. The shipment came into a major port, I hired a van to pick it up, brought a brawny son along, drove there, signed some forms, busted up the palletized load into the van and drove it back home. The whole pick-up process took most of a day.
Heath arrangements vary a lot by country so I won't comment on them much. Getting insurance as a "bridge" is also necessary if you're let in on a short-term visa pending their granting you permanent residency. You also have to avoid getting entangled with the justice system during that period, even minor crimes can disqualify you.
Live like the locals, not like an American. Swimming against the current is exhausting, and you'll soon find out that the thing you thought was essential for you to to live wasn't actually worth having. I've got a smaller house than I had in the US, I drive a smaller car (and drive a lot less than I did in the States), and my fridge is smaller than I am. But my greengrocer's a 5-minute walk from my house, so I don't need to have a month's worth of food in the fridge.
Once you've bootstrapped in the new place, take a vacation, enjoy the new environment. Don't forget who you are, but keep moving forward.
