Advice around persisting app data

I'm looking for some advice on the best approach in storing some data within my app. The app data is structured around a series of Set and Map collections (these collections hold primitive as well as simple object data types).

I want to store the state of these various collections within the app and my question is on what would be the preferred way to store this data? I am looking at SQLite databases but before I go down that road would like to be sure it is the best option.

Thanks.