I will be getting recommendations from several pianists for local piano teachers teaching adults. My question is what characteristics and experience should I consider in selecting a piano teacher?
1)Know your desired focus (and factor in that it can change over time);
-Composition/improvisation (Classically focused)
-All of the above
Often what teachers have to offer will be limited to just one of the above, but there are many experienced with a bit of all.
2)Know that all teachers aren't created equal. Several will be extremely
competent players of varying styles, but that knowledge and experience is useless if they can't articulate and convey it to you in a way that you can understand - determining if this will or won't be the case is the most important thing for you and on this list
2.5)Some teachers will have advanced degrees. All things equal, I'd lean towards someone with a degree. That being said, a degree in Piano Pedagogy (Piano-specific teaching) may indicate that the particular teacher is specifically interested in teaching students for a career and witnessing and partaking in their growth as musicians rather than simply teaching a few days a week as a fallback for extra income
(not that the two obviously can't coincide). This all being said, there are, of course, exceptions to the rule - my teacher being one such degree-less example. I'd be lying, however, if I didn't think my teacher would benefit from some pedagogy studies. In this situation, you're far safer making generalizations than not, especially when less-experienced.
3)Do you connect with the teacher [in your interview/trial lesson]? It's absolutely essential that you're comfortable approaching your teacher about any and all troubles so that your mind can always be at ease and focused on your musician's journey and not various concerns/worries. I list this as number 3 because it can take time and doesn't need to be immediate if numbers 1 & 2 were satisfactory.
Having been in your shoes self-teaching as well as in the shoes of a student with a teacher's guidance, I've come to much prefer the latter. Good luck and keep us posted.