In my apparent role as the go-to coach for "things I'm reluctant to ask someone else about" at my rink, one of the discussions I get is about how to choose a coach for the first time. ("Hey, Xan, we think you're great and Susie really loves you and we're thinking about getting private lessons. Who would be a good coach for her?" I'm not kidding. Um...me?)
Well, not really. I'm glad to be here to field these questions, and I don't take many private students, focusing on the purely recreational group.
So how do you choose a coach?
The first thing to know is what short term and long term outcomes you want. Short term-- learn a specific skill, move up a level, perform in the rink's exhibition or show. Long term-- keep skating through high school, get a solo in the ice show, take the USFS tests, compete. Find a coach who supports these goals.
There's lots of advice about this on the internet, starting at the US Figure Skating site, in their section for parents. But they, and many others, really zero in on choosing a coach for a competitive career. (Some of the questions USFS suggest you ask: "What are your greatest coaching accomplishments? What is your skating background? Do you specialize in coaching certain disciplines (singles, pairs, dance, synchronized skating)? What levels have you passed? Did you skate competitively?"
If you've got a 9-year old Beta or Gamma student who thinks they might want to get better faster, is it really important that her first coach competed at a high level or not? How about a coach who specializes in beginners? It's not even on US Figure Skating's list.
A better place to start is by watching a particular coach's interaction on and off the ice with the kids, with the parents, and with the other coaches. That last thing is a huge indicator of a well-rounded person, let alone coach. Does the coach isolate him or herself from everyone but his/her cronies, students and parents? Does the coach come off the ice after class and talk to a lot of different families, or only some families? Does he or she interact with each student in the class, with none, or with only some?
And of course, most important, does your child respond to this coach. Especially if you are starting lessons before freestyle levels, the single most important skill the coach needs is the ability to respond to your child.
As the old Human Resources trope goes-- Hire the Smile.