A comprehensive answer to this question would be voluminous. In my experience the very best private teachers have the greatest number of students and even a waiting list. "Word of mouth" gets around and folks can find out who the best teachers are by asking others in the music community.Anyone have thoughts on what makes a teacher good (or not)?
In the U.S. band classes are generally offered in public schools beginning as early as 4th or 5th grade. Unlike the UK the term "public schools" in the U.S. refers to those that are state funded and free of charge except for special supplies or activities. Outside of school students at all grade levels can pay to take private lessons in addition to their regular band instruction from either their band teacher or another instructor.I'm not familiar with the US educational system, but the OP asked about private school lessons, whereas the responses seem to be about external teachers.
Teaching the fundamentals of good playing habits and skills are best done by an experienced professional teacher---especially at the beginning stages of one's playing experience.I do not really mean to get more than a year ahead. I am just wondering if he could give me a few beginner tips & lessons.