Best bet would be to use SQLite and have a local database file I think.
This way you could have 2 different databases. one of which keeps track of users with a user_id etc, the other which keeps track of stores and contains a foreign key linking it to the user table.
If you want to keep track of what records you have uploaded to the site just add another column to the table and every time you upload a record you change this value to '1' or whatever.
With regards to detecting who's cheated that's going to be another problem altogether, SQLite has it's own synchronization so you could in theory keep the lock on the database up until the user submits a score and then acquire the lock again? Just an idea but it might add that extra bit of protection and prevent most script-kiddies.