You would in general apply from the country you are residing in. Depending on the country you're going to, you might have to get separate visas if your passorts are different nationalities. If you are married, might be best for her to apply with you as spouse.
You will need a bill of sale (witnessed), signed copies of your and sellers Id/passport bio data, certificate of residency from immigration. You will need to take the vehicle to Pranburi DLT if the vehicle is already registered in Prachuap Kiri Khan province. If another province You'll have to take the vehicle to Prachuap Kiri Khan city. Will cost you about ฿1k. A bit more if you need provincial plates.
Always best to take seller with you too DLT in case any issues arise.
If you applied in country for your non-o then all the timers start at the stamp date of that visa. Your previous visa is now invalid. Since you would either need to apply for your one year extension within 90 days, there is no 90day report due till after you get your extension.
Not sure about SSI, but SSA has no change. Medicare is useless here. Insurance here is also pretty useless if you're older and/or have or existing conditions OR previous treatments. If you're not planning to return to USA, drop part b and keep part a (which is free). Tuck your Medicare premium and any supplemental costs into a bank account and self-insure here. Pay your day to day medical costs out of pocket (relatively cheap) and use your savings if you have a significant issue. You can buy insurance for higher risk activities like riding a motorscooter, etc. but regular health insurance here is expensive and you never know what they're going to pay till it's time to do so.
If you like out the way small family owned resorts and variety of scenery you should go for it. Driving Thai highways is not bad. Cities are the areas that you'll have to be very careful of. And if you can go for a week without turning on the windshield wipers when signaling a turn, my hat is of to you. Seriously, the journey will be well worth it. Anybody can fly from point a to point b and not see or experience a thing. I spent a month driving the whole south looking for where I wanted to live. Having a Thai speaker with you will be very helpful.