My concerns most certainly are not the same as other people on this board. My considerations IN ORDER are as follows with the first 2 far exceeding everything else.

An excellent surgeon, who would perform an excellent surgery

To receive the correct surgery for my specific symptoms
only important for surgeons of equal merit on counts 1 and 2:

Good pain control after surgery

Close to home

Good bedisde manner, hospital stay, etc.
Aftercare/support system was not a big issue for me in LA because I have good support form my husband and our parents who will come out to help us for my surgeries.
Insurance was also not a big factor as I am on my own personal insurance (no worker's comp issues)
My primary concern was to figure out what the right procedure was for me, and then get the best available surgeon to do it. I was unsure if a scalenectomy or a rib resection was the right way to go. Therefore I concentrated on visiting surgeons with excellent technical reputations that did the various procedures.
to save time, I eliminated some doctors sight unseen because I thought that visiting them would be a duplication of visiting a similar doctor. For instance, I eliminated Gelabert and Annest sight unseen because I thoughtthat I attained my goals by visiting Ahn and Brantigbut that is the logic I used not to visit those two doctors. It was nothing personal and there wasn't anything particularly that I didn't like about them.
I approach this by visiting doctors In asking which procedure they would suggest, and why. I
did not expect to talk any doctor into doing a procedure he didn't want to. I figured that the best approach was to pick a doctor based on which procedure I thought was right for me
Using this logic, I visited the following doctors from Mid March until yesterday....
Dr. Filler
Dr. Ahn
Dr. Weaver
Dr. Brantigan
Dr. Sanders
more to come....