Ok, I really like taking random notes but my teacher hates the fact that I do. She says I need to pick a note style.

What style is similar to random but has something.

I don't know the answer, in detail, to your question; however, I think it should be irrelevant to a teacher what note style you use as long as it's a winner for you. Anyway, my teachers always covered so much material that I had little time to worry about the style I used; I just concentrated on getting everything down. Perhaps that's why my notes always looked disorganized.