There's quite a few different surgeons, but a few big names. Personally I think its important to look at the quality of their work. You can find a fair number of photo's online, just not as many as you'd like. You might also like to consider how often problems occur, how serious they are, and how responsive the surgeons is to looking after you post-op.
There's a fair bit of variation in price and in wait list time. Some surgeons have a wait list of a few months, others 2+ years.
You could spend a lot of time reading this site, and searching with generally google. There's a huge amount of information out there.
Work out what is important to you. Perhaps you don't want to travel, have a financial limitation, health issues, want it done now, etc.
Someone wrote up their experience going to one of the Thai surgeons, and it might give you some idea of what to consider.
https://www.the-ress.net/files/SRS-With-Dr-Suporn-2015.pdf