I would recommand to use the sqlite
Database. This storage is persitent across killed processes and is only private accessable from your App. Have a look here for a first introduction.
SharedPreferences
are desigend to store primitive data types, so you cannot easily store nested dictionaries.
The SharedPreferences class provides a general framework that allows you to save and retrieve persistent key-value pairs of primitive data types. You can use SharedPreferences to save any primitive data: booleans, floats, ints, longs, and strings. This data will persist across user sessions (even if your application is killed).