In my town, a lot of the culinary students get kits that the school puts together. For people in baking & pastry they have a roll for knives and a roll for baking stuff. I would go crazy dragging all that crap around in different bags.
Keep in mind that you have to keep it somewhere once you get to class. Travelling light is usually a good idea. Juggling a lot of stuff gets distracting, and trying to store it in a kitchen without enough room is frustrating. The Chefpak mentioned above is designed for people in your situation, and if it holds everything you need, it might be a good solution. I find portfolio style knife bags great. I use the big Ultimate Edge bag. It is a lot less cumbersome to get into in tight quarters than the roll type bags I've used before, and it holds a lot of stuff. Notebooks? Yes. Textbooks? No. A good question is, do you really need the textbooks in class? My knives get Forschner clamshell type guards. Big knives get Dexter slide on guards. Shears have a cardboard and tape guard. Gadgets with guards and handles go into my knife slots, other gagdets, peelers, whatever go into the big mesh pockets in my bag. So far nothing has been damaged.
I'm not a culinary student, but if I were going to school, I would try to carry the same gear that I use in a real kitchen now. I would try to avoid getting a big rolling case unless no other solutions work because I can't handle dragging around and dealing with something that clunky. Everybody's different though.