I truly believe and understand that energy is more fundamental than work &
"should" be introduced first. But I still don't know how. My beginning
students know what force & displacement are, so they can understand work,
and then I can show them that 1/2 mv*2 or 1/2 kx*2 or even mgh equals work
done (I know, I know, I'm careful). But if I start with energy why
shouldn't it be mv*2 or mv*4, or why not mgh*2? The only 'proper' way I
know is to start with the expansion in power series of v/c of the
time-like component of the covariant 4-vector ....!!? Or Noether's
theorem!!?
Work is easily defined. Energy is not .. it's just something that we can
always find some way of accounting that makes it conserved.