Someone from Thai immigration will check your passport after you get off the aircraft. Then if all is OK, they will put a stamp in your passport for 30 days visa free in Thailand. Then you can collect your luggage after that. 😊👍
Don't use an agent if you want to stay in Thailand seriously. If any law changes or agents are abolished you will not be able to renew, and will have to leave. Best to just save up and have peace of mind if you really want to live in Thailand.