if you marry then you don't change your visa as such just what your next extension is based on at renewal time. 400K for marriage versus 800K for retirement, more paper work for marriage. If you are on an OA visa and extend based on marriage you don't need health insurance.
In my case it was blue book, housemaster present, girlfriend present, passport translated into Thai, letter from immigration, two government employee witnesses to attest I live there.
Try Kasikorn my wife and I opened a joint account no problem, take your original marriage certificate, blue book, yellow book 'if you have one' and all ID
You have two clear choices for visa non immigrant based on marriage or based on retirement. Marriage less money in the bank , more paperwork, retirement more money less paperwork. I have used the public health system not free for foreigners but cheap and have had good experiences. You should have private insurance incase it goes horribly wrong