Each school can decide if they would like students and/or teachers to login with an Apple ID. The main reason someone would want to login with their own ID would be to download apps and/or make purchases. We recommend that you do not allow students to login, but you do allow teachers to login - that is now the default profiles are configured, but you can change them if you like. If teachers do not need any apps other than the apps you deploy, then they do not need to login with their own ID. But they certainly can if they want to.
I would strongly recommend against using shared Apple IDs. In order to create an Apple ID, it needs to be associated with a credit card and you would not be able to tell who made a purchase if the Apple IDs were shared.