What start date should I choose for Thai health insurance for my O-A extension of stay if I apply on October 20?

Make sure you are covered by the policy on the date you GO to the immigration office to apply for your extension. Unfortunately I have not found any insurance company on the list of the 14 companies that will pro-rate a policy (OR that will take more than one year of premiums either) so that means you get a year policy and you can only select the date it starts. :/ IF you start it 2 weeks before your extension expires it means you will not get a full year extension (they will only give you an extension for as long as your policy is good for so if you start it 2 weeks before your current stamp expires you'll lose 2 weeks on the extension you get)

Some (if not all) insurance companies will give you 13 months on the OA insurance (one month priced pro-rata), so you have flexibility to have the insurance run from the date of application through to the expiry date of your visa or previous extension.

Before you go to Immigration.