The Non-OA is a poor choice of visa in my opinion.
Not only do you need a doctor exam and criminal records check, but next year you can only renew your mandatory health insurance with one of 14-16 approved Thai health insurance companies.
Unlike America, the insurance companies don’t have to accept you. Any major preexisting health condition, or simply being overweight can result in a denial of coverage and loss of visa.
With a Non-O visa, you can secure health insurance from any health company, anywhere in the world… or choose to self ensure, or no insurance at all.
The Non-O visa (which in my opinion is preferable for most, if not everyone) does not require health insurance.
However, most would recommend you purchase travel insurance, which is inexpensive and available for up to a one year term, from major companies such as WorldNomads or Allianz.