i am planning a 120 day trip to buri ram. what kind of visa do i need. i am 65 and thinking of moving to thailand

Hi all, I’ve read through a lot of questions to get a better idea but want to make sure I’m understanding.

I will be arriving in Bangkok Sept1 with a 30-day VISA exempt. I would like to travel (Chiang Mai and perhaps an island) around until I start teaching in Buri Ram Oct. 1.

So my concern is with my 30 day exempt stamp will I be able to go from province to province or exit and renter Thailand? And then once I get my new Visa I planned to just cross over to Cambodia to activate it, is that correct? I do have a plan to go to Singapore also Oct 4. So just wanting to make sure I’m understanding the re-entry process.

And I should find the local immigration office in Bangkok to fill the Form 30 when I return from any adventure or wherever I stay..?