Nice tutorial! Some notes:
Right now you're connecting to the sqilte database twice - a second time in the T_Connect callback using the non-threaded SQLite_UseDatabase while leaking the first database handle.
You don't really need to check the database driver unless you want to run some driver specific queries (like AUTO_INCREMENT in mysql vs. AUTOINCREMENT in sqlite)
You should never try to get the steamid of a player in OnClientPutInServer. Always use OnClientAuthorized to avoid STEAM_ID_STOP_IGNORING_RETVALS in your database AND always check the return value of GetClientAuthId.
There is a superceding Database methodmap interface you could take a look at. Especially the new
Database.Connect function and the new
callback prototype. This will save you some of the retagging when saving the database handle.