Personally, I prefer traveling as light as possible. My favorite setup is a large backpack with enough room for my essential gear, along with a carry-on packed using vacuum compression bags. This is the bare-bones option and works well if you do not want to check luggage or drag a lot of stuff around Thailand.
If you want a little more room, especially if you plan on bringing things home, go with one carry-on, one large checked suitcase, and a small backpack for your personal items. Even with the extra luggage, I would still pack light. Thailand is an easy place to buy clothing, toiletries, and anything you realize you forgot.
One thing I would not skimp on is underwear. Bring plenty. If you run, wear sneakers often, or are not the type to live in flip-flops, bring a good amount of socks too. Between the heat, training, and sweating, you will go through them quickly.
Keep your Muay Thai gear to a minimum. Bring what you really need for the first few training sessions, but remember that you are going to Thailand. Gloves, shorts, hand wraps, shin guards, and other gear are easy to find there, and buying some of it during the trip is part of the experience.
