I've always cycled to work/school/classes and I've always just carried a backpack. I never bothered taking text books with me, but usually carried laptop (not the teenyweeny type), notebooks, food, snacks, sweater/jacket and sometimes even some work-out gear. Just a normal school bag type backpack seemed to work well for me. If it got a bit heavy the hip-straps helped take the weight off my shoulders. I've had anywhere from 2-40 minute commutes depending on where I was studying and where I was living. Seemed to work ok for me.

If you insist on going with panniers I know there are several that come with back-pack type straps to be carried as a regular back-pack off the bike.

An option for lockers is to check out the gym on campus. Most places I've been a student, they have lockers for rent at the gym.