MuseScore is ideal for use in a classroom environment; it's easy to use, immensely powerful, and can be installed for free on as many computers as you need. You can easily use it for homework assignments, as well, since your students can also download it for free at home. A number of schools and universities already use MuseScore.
If you're a music teacher using MuseScore with your students, a MuseScore.com private group is an ideal way for students to turn in assignments securely and for you to communicate with them. When creating the group, check the box for "Private group" to keep your students safe, then use the "Invite people" button to send them an invitation to join the group. Let them know how to make their uploads private (see Privacy) and add them to the group (see Sets and groups). You can comment directly on their scores and post announcements in the group's Discussions section, and they can update their scores in response to your feedback.