Which visa should I choose for a 3-6 month stay in Bangkok: the destination Thailand visa or the multiple entry tourist visa?

If 3-6 months visit is all you want, you canb choose between visa exempt or METV.

DTV is for 5 years, more expensive and more requirements, but has advantage you get a stay of 180 days each time you enter.

Visa exempt is free by itself and valid for 60 days if your nationality is eligible.

After 60 days you can choose between getting 30 days extension at immigration for 1900 baht or do borderrun and get new 60 day stamp. How long this scheme is working depends on the immigration officer.

When you apply for METV you get 60 days each time you enter during the period the visa is valid, you only have to get out and back in each 60 days.

This method has far less risk of getting stopped by immigration.

Do not get the multiple entry unless you plan on leaving every 3 months.

Why not get an education visa?

You’ll need 500k baht in a bank account in your name to be eligible for the DTV

METV can get about 9 months in Thailand. Each time you enter Thailand you can get a 60 day entry stamp and a 30 day extension. You can do this 2 times then just before the visa expires you can do it one last time and get another 3 months for after the visa is done.

That's 60+30, 60+25ish, 60+30.

If you only need 6 months that should be plenty, but as you stated you will need to do at least one border bounce. They run about 3-4,000 baht if you use a land border bounce agency to drive you there and back. Or if you can find a cheap plane ticket to somewhere that doesn't charge your nationality for visa on arrival, you might be able to do it cheaper yourself.

A DTV would get you a flat 180 day entry stamp on each entry and it costs 10,000 baht.