What are my visa options for a 66-day stay in Thailand with visits to Laos and Vietnam?

You will get stamped in for 30 days visa exempt. This can be extended by a further 30 without leaving. If you go and come back, you get stamped in for another 30 when you come back. Depending on your travel plans and how long you plan to spend in Laos and Vietnam you likely won't need a visa in advance. The only thing to bear in mind is that there is a limit of 2 land visa-exempt entries per calendar year but you are unlikely to run up against that.

You will need to apply for a visa for Vietnam online before you go there. You can get the Laos visa on arrival (either airport or land border). Visa fees for both are best paid in US dollars.

Visit the website of the Thai Consulate or Embassy in the country where you are at the moment. Look at all the visa options, choose one that fits the requirements and lenght of permitted stay in Thailand and apply for that visa.