Calling a final or private method from a constructor is always fine, and yes, it's good style if it reduces duplication or makes the code more readable.
Calling a non-final/non-private method -- specifically, calling a method that might be overridden -- is something
you should do carefully. That's because when a parent class is being constructed, it will call the child's overridden version of the method. Sometimes that's exactly what you want -- it's a way for the child to customize the construction of the object. Other times, it's a bug waiting to happen, or even a security hole -- so be careful!