I find it strange that some things aren't stated about working as a teacher in Thailand. Firstly, if you are contracted directly by a government school, they are legally required to enrol you in the social security scheme, the teacher paying one part and the school paying also. This will cover all medical expenses in a government hospital and it also pays towards several other benefits such as childbirth and some unemployment payments and over the long term, a pension. Should you then decide to work in non-government school, or heaven forbid for an agency, you can move over to self-payments, which are about 450 baht a month, and retain medical cover and pension.
I know this because I had a heart attack, and received full ongoing treatment for free. Plus if you return to your home country, you may also get a lump sum of the pension payments you have made. Also paying tax will also see you have a tax rebate. If you are married and have other expenses, most tax offices will be happy to help you. Be wary of some agencies stating they only pay for less than a year. Most will have received the funding for the whole period and the other legal requirements of a government school. If injured at school, the school are responsible. Don't let them tell you otherwise unless the agency can show/give you insurance details while you are at work.