My approach to much of this has been be-labored in past incarnations of
this thread. Let me this time add that an approach which I have often
(fruitfully) taken is to immediately follow Newton's laws with the
impulse-momentum theorem and the consequent conservation of linear
momentum (this is "naturally" motivated by the students' queries about
N3).
After this exploration of the implications of the TIME integral of F=ma,
it can be made quite "natural" to investigate the SPACE integral of N2.
Thence to the work-energy theorem, conservative forces . . . etc.
My motivation is to lift as little as possible "out of the air", but to
rather explore in a somewhat "natural" manner. But at the same time, all
of this is preceded by the admission that our intuition is not really this
clever . . . we are using the hindsight provided by the giants upon whose
shoulders we teeter.