I went about it as if I were hiring a new employee for a very specific and highly skilled job, because in many respects, that is in essence what you are doing.
I'm a very analytical and clinical minded person, and how I chose my SRS surgeon was no different. You want to find out where they went to med school, are they licensed and board certified in cosmetic and plastic surgery, what they specialized in during their residency, what hospitals they have practiced at, how many procedures have they performed, what if any are the major complications they've run into, do they have malpractice insurance, look at as many before and after pictures as possible, what is their after care protocol, are follow up visits and any needed revisions performed free of charge, what age/weight/health restrictions they have, what preop tests do they require, what are their payment/deposit policies, what sort of postop accommodations are available, what hospital do they normally operate out of, and talk to as many of the surgeon in questions past patients as possible. There are other things to look at, but this is jut off the top of my head.
Just like when you hire someone, you want to select the best candidate or the job... Just not settle for the first one that applies, is available, is the closet or cheapest. Take your time and do your research.
When I had my list narrowed down to 3 surgeons, I scheduled face to face in person consults with each one.