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I think a more pedagogically valid approach is to start with momentum, in the from of collisions. This is a very concrete approach that students can get a "hand-on" feel for. We don't need the details of the collisions, just the before and after information. This can lead to the concept of force as "the thing needed to change motion," and the collisions lead pretty naturally to the Third Law. A more careful approach to considering force in collisions can suggest the Second Law, and then bringing in the First Law as a logical consequence to the other two and make the connection with history.
I'd like to see comments of a proposed re-ordering of topics that I've been thinking about. In the topics of gravity and electricity we usually introduce the forces first. For gravity we start out with the force that a planet (usually Earth) exerts on a mass, m, and state
F_ = mg_ (the "_" indicates a vector).