Chiang Rai has 4 main hospitals. Overbrook, a private christian hospital founded by missionaries about 100 years ago. Sriburin, a newer private hospital which is favored by most expats and the newest called Inter Hospital. The government hospital is far more basic than the other two and much less expensive. Then we have the government teaching hospital at Mae Fah Luang University but the services there are limited.
As for the doctors, it makes no difference which hospital you choose because the same doctors rotate through all of the hospitals.
Depending on your needs, health insurance can cost anywhere between $1,000 per year for coverage in Thailand only to $3,000 plus per year for international coverage. Unless you are a frequent traveler, you probably should consider the cheaper option and purchase travel insurance as needed. We will be happy to connect you with someone who will take care of whatever you want health insurance wise.
I know of no insurance company that will accept anybody over the age of 70 but if you purchase before turning 70 it is possible to continue renewing the policy.
I am aware that most countries sell a health insurance policy that covers all family members but that is not so in Thailand.