Some glaring points not addressed
1 very situational and student specific
Ex student just beginning to learn from scratch vs a student ready at the say early advanced level (ie could successfully audition and gain admission to University or conservatory level based on difficult , volume , and refinement of repertoire performed)
Proven track record with say children and adolescents vs adult (vs young vs older adults ), the brains are different so there should be proven success with each type of learner
Value proposition - affordability is relative , however unless there is such demand to enter the studio that it is competitive enough to routinely turn away fairly gifted students ,the tuition should be appropriate to the microeconomics of the local market , again track record of say producing consistently successful competition winners and audition to competitive programs , that must be documented with success so far as pricing vs market rate is set
The best teacher should be able to be connected with other studios and can refer a student if it isn't either working out after sufficient time and study ie is someone else better suited to help them despite appropriate effort from student and teacher , ie I think I know someone that can help you even better than I could , I want what is best for your particular success , ...knowing and acknowledging your limitations to not accept a student you feel confident of benefit more from someone else's style or of teach or way studio is or school is run betc