To start, I'd download a (free) copy of SQL Server Express, except it won't run on a Chromebook, I'm afraid. So first question:
Is you school providing a SQL Server database you can connect to?
Also:
Do you have the barcode scanner and whatever software goes with it to actually scan the codes and save them to a file somewhere?
Once you populate the database with the Student ID's, what then? Will you be building reports or something to get the data out of your database?