This depends on how long you want the data to persist. Ask yourself:
Should this data be available to the users after rebooting the phone, or after force closing the app? Should it be available regardless of the last time I had connectivity, as up to date as possible given that?
In that case, then yes - you should use a database. Android has a number of built in helper classes for sqlite databases.
http://developer.android.com/training/basics/data-storage/databases.html
Which should get you started.
The images are pretty straight forward as you'll just stash a reference to the image(s) in the db. You would of course write these images to disk as well (on the sd card or some other place...) See:
Your other options, afaik are:
1) SharedPreferences (not really suited to this).
2) Serializing your data and writing out/reading in from some file.
If you're still looking for more information on Database concepts and Android, here is a very good tutorial on the topic: