I would go with a wheeled (rolling)case, especially for taking to classes. I am taking classes as well. My sewing machine goes into a wheeled case, then I carry another large flat bag with my cutting mat, rulers, etc, I also have a third case I carry with my fabrics/projects in that is styled like a large briefcase especially made for transporting sewing/quilting projects and tools. You won't regret getting a rolling case for the machine.
DeeDee