My style of teaching places emphasis on technicality before musicality. I spend copious amounts of time in lessons trying to avoid bad habits and chunking pieces of music. This involves splitting music into small phrases which are practised and repeated independent of each other, and then finally put together as one beautiful masterpiece.
My basic lesson structure is to spend some time on technical work at the very start, including scales and studies, then working on the technicalities of pieces of music, such as particular chunks which aren't quite polished, and finishing with fun music as an enjoyable end to the lesson.
In terms of style of music that I teach, I can do anything from classical to pop and rock if you'd like! Overall, I tailor my teaching style to the learning style of students (visual learners vs. practical etc...), as not everyone thinks the same, but I try to keep a consistent lesson structure, with some flexibility.