Can I apply for a METV after entering Thailand on a tourist exemption visa, or should I get it before arrival?

𝗙𝗿𝗼𝗺 𝘁𝗵𝗶𝘀 𝘃𝗶𝘀𝗮 𝗰𝗮𝗻 𝗜 𝗮𝗽𝗽𝗹𝘆 𝗳𝗼𝗿 𝘁𝗵𝗲 𝗠𝗘𝗧𝗩 <- no you can't get ANY tourist visa inside the country.

You get an METV from the thai consulate in your country before you come here. So yes I'd say that your 𝘀𝗵𝗼𝘂𝗹𝗱 𝗜 𝗷𝘂𝘀𝘁 𝗴𝗼 𝘀𝘁𝗿𝗮𝗶𝗴𝗵𝘁 𝗳𝗼𝗿 𝘁𝗵𝗮𝘁 𝘃𝗶𝘀𝗮 𝗶𝗻 𝗺𝘆 𝗰𝗼𝘂𝗻𝘁𝗿𝘆 is the correct answer and you should get a 6 month METV before you come here. That visa will let you get almost 9 months of stay out of it if you work the dates you bounce out and back correctly

As far as the looking into the ED visa, the place to do that is at the school you're thinking of enrolling in