I have the 1-year non-OA visa and the application process was relatively straightforward.
For the mandatory health insurance, I recommend purchasing from a Thai agent/insurer to avoid any issues with meeting the requirements and the proof of insurance documentation.
When I arrived in Chiang Mai, the immigration officer requested proof, and I showed the complete Thai/English policy plus the receipt page with a red "PAID" stamp. Make sure to tell your insurance agent that the policy must meet non-OA visa requirements, as there are specific minimum coverage amounts that need to be met.
If you plan on being here a year and WANT health insurance, there are Thai insurance brokers or insurance companies that can help you get sorted. I used AA Insure, though there are others.