When I was 17 I had to have mine cut and extracted out. They did put me under but very very mildly though. I wasn't out all the way. I was sedated enough to not be bothered by what he was doing to me but was very aware of what was going on.
I would go with the one that has very good experience. I would also go by word of mouth. I went to a great surgeon but my dh went to one that we would never recommend to anybody. I didn't like her at all. He developed infection. After a few weeks, I heard from others that she is NO good. So it would be good if you can ask others in your church, homeschool group and so on to get a good feel of which one would be best. You can also interview them as well.
Holly