should each individual on a family plan have their own ICloud account?

Yes, that's usually best. Otherwise all your synced data is merged, you will all share and back up to a single free 5GBs OS storage and share a single iCloud email account, etc. You can do this and still share the same iTunes ID (it doesn't have to be the same as your iCloud ID).

ALSO, don't use the same ID for iMessage or FaceTime. Otherwise you'll end up getting each other's text messages and FaceTime calls. Instead, use your separate iCloud IDs for these services.