I am currently looking into making a basic video game. I have programming knowledge in Web technology, but not much in Android so I am most likely going to start by making a Web app on Android.
I haven't used Web storage much in the past, but I do know about local storage and indexed db, which could be considered as a way to store data, but this kind of data seems too easy to delete by mistake because people just generally wipe out Web data once in a while without filtering out important data.
What is the most appropriate way to store Web app game data?
The storage type relies on the characteristics of the data.
Since you want an approach more user-proof, I prefer the SQLite approach. Be aware that no method is 100% guaranteed, since rooted phones can grant access to physical data. At least, consider to encrypt sensitive data before sending to the database.
You also have the option of hosting a web service that is consumed by the app to gather information. It can be a lot safer, it is easier to be accessed by all instances of the application, but introduces internet dependecy.
Hope it helps.