Since one of our requirements is that this solution should work, as far as possible, without a connection, and where not, with only a connection to the local network, our project will consist of a locally hosted ASP.NET Core API and a UWP application. Each person that needs access to this application will be given a tablet where they can either check or update stock. The architecture of our system will look something like this (not exactly an original architecture):
The UWP client application app will be given to all members of staff, which means that, in addition to authenticating the user, the application will need to prevent certain users from accessing certain functionality.