Interface 1 (e.g. Tab): will deal with orders, mainly placing them
Interface 2 (e.g. Preparation and Packaging, using a simple monitor, no input required): what they need to prepare and pack shown in the monitor
Interface 3 (e.g. Manager, PC/web): Looks into inventory and supply.
Question is how to have these multiple interfaces for multiple roles with multiple tasks under each on a single Meteor JS app?
I think you want to look into using the alanning:roles package: https://atmospherejs.com/alanning/roles
That will allow you to allow/disallow access to actions/interfaces by roles you define and give to users.