people are soft spoken here, everything moves at a slow pace, crime rates are low (besides drugs at the golden triangle), barely any traffic jams, plenty of great mountains. Just a perfect place to retire.
They will give you an appropriate visa once you have all the full documentations from the school and government. No walk ins allowed, you will have to make an appointment online, submit all the documents they need online and they will give you an appointment date.
Stay 2 days in Malaysia, Penang would be the first choice if you can drive down for 2 hours after the border. If you cant, just stay in Chang Loon, nothing much there though. Get your car insurance done at Dan Nok. I drive from Chiang Rai to Kuala Lumpur frequently.
To simply answer the question, 1-2 months will be best or until the permitted time in the other country is about to end. That will make you look more like a 'tourist', because that is what most tourists do.