MS Access will work just fine for this kind of thing! In broad stokes, you'll basically need two Tables:
StoreID (Primary Key)
StoreID (Foreign Key)
You'd then use tblStores as the RecordSource for a Main Form, and tblProducts as the RecordSource for a Form to be used as a Subform on the Main Form.
When you add the Subform Control to the Main Form, and select the Products Form as the source, Access should automatically join the Main Form and Subform using the StoreID Fields in both. When you add a new product Record to the Subform, Access will automatically populate the correct StoreID in that Record.
A single Record for each store will be in the Main Form, with one or more product Records, per store, in the Subform. As you move from store to store, in the Main Form, the products in the Subform will change, appropriately.
Welcome to dBforums!
Hope this helps!
The problem with making anything foolproof...is that fools are so darn ingenious!
All posts/responses based on Access 2003/2007