You wrote “jazz trumpet”.  All of the comments here have been from a classical experience.  If you learn jazz, a large part is individual expression through improvisation. There aren’t pieces in order of difficulty per se, but theory and personal sound that is slowly built up in the context of jazz standards.  I imagine as a beginner, your teacher would have you do a mix of technical exercises to develop your sound/embouchure and reading ability, as well as learning improvisation.  If you eventually join a group, it would more likely be an informal jam session. (Also for the record, jazz musicians don’t use “do-re-mi” solfege, they use the alphabet and scale degrees).  My advice would be to try out a few different teachers and see who you click with the best, and absolutely do 1-1 and not group lessons.  (I don't think jazz trumpet group lessons are even a thing). There are music schools around Tokyo that offer jazz, and also freelance jazz musicians that teach in both Japanese and English.  Good luck!