Just do it how you want to, no one will force you to do anything, there might be some teachers that don't like laptops in their lessons, that is dependent on each separate teacher. Personally I wrote everything down with pen and paper, but a lot of students use their laptops and Ipads in lesson, dont worry either way you'll be fine.
You can use binders to keep your own notes and classwork etc sorted, i just have loads and loads of plastic wallets where I store all my notes as I look at them frequently and I keep them close by. Binders will also work, just do what is best for you.