We just started violin lessons for my 6 yo perfectionist. I'm not a musician either though, so take my experience with that.
We chose completely private lessons rather than group, with the plan to add an ensemble later once DS gains some confidence in his own abilities. We also wanted DS to have an activity where he controlled the pace completely---unlike school, where he just goes through the motions as he flies ahead of his classmates. (;
So if he works and practices during the week, he moves on. If not, he moves more slowly.
We felt that a big part of success would depend on a match in teaching style. We interviewed a few teachers, and I think we have found a nice match. His teacher gives him a lot of praise for small things, and corrects him very, very subtly, cloaked in praise. And he has longish hair and is very cool/hip, so that helps too. LOL. I'm quite sure that the teacher is also gifted and a perfectionist by personality, so they get each other.