No, you're not on the right track. A good rule of thumb is: make everything as private as possible. This makes your class more encapsulated, and allows for changing the internals of the class without affecting the code using your class.
If you design your class to be inheritable, then carefully choose what may be overridden and accessible from subclasses, and make that protected (and final, talking of Java, if you want to make it accessible but not overridable). But be aware that, as soon as you accept to have subclasses of your class, and there is a protected field or method, this field or method is part of the public API of the class, and may not be changed later without breaking subclasses.
A class that is not intended to be inherited should be made final (in Java). You might relax some access rules (private to protected, final to non-final) for the sake of unit-testing, but then document it, and make it clear that although the method is protected, it's not supposed to be overridden.