We only shipped what's sentential for us which are mostly books. I found the furniture here are actually better in quality and prices, most rentals are also furnished. I don't miss anything I left behind, but my husband is 6'2 so he wishes he had bought more pants that would fit him. We ended up bringing 50 boxes, of which 40 are books/art books. I highly recommend Asian Tigers for international shipping. They made the whole move very easy.
Rentals are done on the ground for sure. We contacted agents a few months before our move and every agent said it's too soon. Even with a dog we found a place within a month of moving here. It's also better to get to know the city in person before deciding what area you want to live in.
Where in Thailand are you looking for rentals? What city? I paid 15,000 a month for an apartment when I first moved up north, I had a small kitchen and laundry machines in the facility. Now I pay 20,000 for a house with everything, even an oven. Thai people can, and do cook all the time, as well as do laundry themselves. What you are finding is not a culture issue, it's an affordability issue. What can you get with $350 per month in the US? A rental space for your car? Thailand is cheaper than the US but you also need to be realistic. Raise your budget and you will find plenty of rentals with modern amenities.
I visited more than 10 house when l was looking for a rental. Every single one had a kitchen and washer. dryers aren't that common because most people hang their laundry to dry.
China, Japan, Korea and Taiwan are not in SEA. Do you mean Asia or SEA? Most countries in the world won't allow foreigners to live there long term without proper visas. Look into which country allows you to live long term should be your top priority. If you don't mind moving around every 3-6 months, you will have more options. I personally would not recommend China or S.Korea. Taiwan and Japan are amazing, and Thailand and Vietnam if you want to be SEA. But all require visas for long term stays.
I personally did it. I had a 5 year residency visa which could be turned into a 10 year one. Not as easy with other Schengen counties but easy with Portugal. Portugal also offered a 10 year golden visa program for any foreigner buying a property over 500k. But they took that program away last year because they are in a real housing crisis with all the rich buyers from other countries. Elite visa is the best solution for easy long term stay but it's still a glorified tourist visa.