I think that the teacher problem has many sides but now you are interested only in some of them. :-)
For me the learning strategy (mainly) depends on seeker’s or student’s skill. I think that sooner or later you should find a good teacher free of charge and I wish you good luck at your way. :-D
I try to illustrate my ideas by my own mathematical way. By the way, :-) you can overview it in my profile.
Personally I never had a tutor, never paid to teachers and I had the opposite problem: to free myself from the classes. :-) But I was powerful – I was one of the first students in my country in school math competitions.
But even already in my high school my school teacher, Volodymyr Prokip said to us that if anybody wants to know a subject deeper, then catch me, grasp my button and ask. :-) I remember as we were walking together along some kilometers from the school and were talking about matrices. :-) Now we are working in one institute and his room is placed in a couple of steps from mine. :-)
Personally I think that a bad teacher tries to find followers, but a good teacher shares with you his methods and strategies which you can use for solving you own problems. :-) I was lucky to find good teachers in my university (but, despite I think that the teachers from my university are good mathematicians, I still avoided the classes, :-) because their level was too low for me and the curriculum was bounded). I am grateful to prof. Taras Banakh (who is now my scientific consultant for the “Doktor of Science” thesis), under the influence of which I was fathomed into the idea to understand instead of selecting through methods, as jimmies, searching which of them can solve a problem. Banakh is still followed by apprentices observing his work and able to learn from the method «do as I». :-) Also I am grateful to my scientific advisor for my “Kandidat of Science” (PhD) thesis, dr. Igor Y. Guran. When I was working for the thesis, we tried to solve his mathematical problems, using my powers and his experience. I.Y. recommended to me directions of development, helps me with advices and as a reference book. :-) And he still does these. For instance, recently I sent to him my «The referee confession». :-)
Further, there should be scientific mathematical schools consisting of teachers, masters and their disciples and apprentices. For instance, I am a mathematician from Lviv topological school, which has the genealogy going through Karl Weierstraß and Carl Gauss to 17th century. :-) And the line of the school is to be fathomed by a seeker.