Public members of a class A are accessible for all and everyone.
Protected members of a class A are not accessible outside of A's code, but is accessible from the code of any class derived from A.
Private members of a class A are not accessible outside of A's code, or from the code of any class derived from A.
So, in the end, choosing between protected or private is answering the following questions: How much trust are you willing to put into the programmer of the derived class?
By default, assume the derived class is not to be trusted, and make your members private. If you have a very good reason to give free access of the mother class' internals to its derived classes, then you can make them protected.