If I have Game Objects and a Game Object Manager, both of which handle the Model side of the Game Objects, then should I compose Box2D into my objects or make my objects build upon the Box2D objects.
I generally have the Box2D object as a property of my game object (because an object's physics behaviour is quite naturally a property) and the Box2D world object as a property of my game level (which may or may not be the same thing as your game object manager - I'm not quite sure what you mean by that).
For each object, ask "does this object correspond to something within the Box2D environment"? If the answer is yes, add that something as a property.
The tutorial st33d linked is a good starting point, but be aware that Box2D's "debug draw" facility (which the tutorial uses) is doing some of the hard work for you. You will need to extract info about the position and rotation of each object once per frame to use as input to whatever drawing procedures you employ.