I\'m making a php web application which stores user specific information that is not shared with other users.
Would it be a good idea to store some of this information i
If you only want this data available during their session, then yes. If you want it available tomorrow, or 4 hours from now, you need to save it to a database.
Technically you can modify the sessions to have a very long lifespan, but realize if they use a different computer, a different browser or flush their cookies they will loose the link to their session, therefore anything serious you should create a type of user account in your application, link the session to their account and save the data in a permeate place.