What happens to my Non OA visa after the first renewal in Thailand?

You're getting way ahead of yourself.

If you get an OA Visa in your country before you come here, you'll get stamped in for a year (or as long as your insurance is valid for up to a year) when you show up .

The next year before the Visa itself expires, if you get a new year of insurance and you exit reenter the country you will get another year went stamp.

Most people get almost 2 years of stay out of an OA Visa that is valid for one year.

You wouldn't need to start transferring money in until the beginning of that 'second year' so that you could use monthly income by transfer method for proof of funds, get a year's worth of the mandatory insurance and apply for an in-country yearly extension at your immigration office.

My advice to you, just get the OA visa, come into the country get the year entry stamp and don't get caught up in what you need to do for your first yearly extension which of you work that OA visa right will be your 3rd year in Thailand