When I haul my stuff to teach a class, it's very helpful to have a shoulder strap. I can carry more things with my shoulder, than with my hands. I even made a portable ironing board with a shoulder strap.
A co-worker gave each of us a plastic tote with a handle on top. Inside, it has a sectioned tray in the top and lots of room in the bottom. Even though it doesn't have a shoulder strap, I really love it!