You can apply for a nonimmigrant O visa. 90 days then you extend yearly. You can buy single or multiple re-entry permits if you travel outside Thailand.
You can stay in Thailand indefinitely, without leaving the country, with either the O or OA. With both visas you eventually get to a point where you are extending your visa 1 year at a time.
You cannot switch from an OA to an O. You will have to wait 1 year for the OA to expire and then leave the country. You then start the process for an O from scratch.
You need to be over 50 to get an OA. Other than that and meeting the final requirements you just live here on it long term. Often considered a retirement visa.
If US citizens arrive without a visa they get a 60 day visa exempt entry like many other countries.
The OA visa is one of several long stay visas. You can only get an OA by applying from your home country. It is a 1 year multiple entry visa. It has a variety of requirements including the need for health insurance coverage.