Start with the easy one...
From another thread on 'which Paganini Caprice should I start with,' several of the commenters said "X is easiest, but I started with Y because I liked it," and the next logical question is, Do you start with a piece on your level, but aren't excited about, or go just a bit beyond and really love working on it?
I think about the time in junior high when I was assigned Scene de Ballet, which was in line with my current level, but so awful to me. I never practiced it, so my teacher worked on it with me longer than he should have.
As a teacher, I never forgot this, and always give students a lot of latitude when it comes to choosing pieces. And honestly, they always manage to meet the bar, even on the stretch pieces. Thoughts?
Well, forcing kids to learn what YOU want is a great way to make them quit—which is why I have so many friends who shot up in the levels young, dropped it, and now tell me how envious they are that I stuck with music. I always played what I wanted to play and so I got the most out of my time with my teachers. The compromise was that I would learn the etudes necessary for my exams... but even then I'd have my choice out of a set.
My daughter just finished a camp online where mostly 12-14 year olds many were given Paganini Caprices. Most for the first time. You could see they were totally energized by the opportunity, and more of them than I expected pulled them off. My daughter did the 15. The teacher assigned them to address issues in the audition tapes, my daughter’s octaves in her case. Really worked for her!
I’d say, it depends…
I once refused a piano piece on the grounds that it was childishly trite - Haydn or something, and my teacher said, OK, but I only ever give my students one refusal. That taught me to respect her will and the seriousness of what we were doing.
As an adult returner, I like to choose SOME of my own music, but I'm always glad when my teacher suggests something at my level or a little bit above when it's something I've never heard of before. One thing I'm paying for with my lessons is my teacher's vastly superior knowledge of the repertoire.
As a teacher, once students are past about the Suzuki book 4 level, I usually give them a choice between two or three pieces at their level (I'll also allow the occasional piece veto in books 1-4). That way they have some choice to pick the pieces they like the most, but are not stretched too far beyond their abilities. I will always consider any piece that a student suggests, but if I think a piece is too much of a stretch I will try to find something by the same composer or in a similar style to learn first.