I want to cut up vs. pieces of plywood and
chipboard for utility shelves (have the sides,
need the shelves.)

The old (not old enough to be good I suspect)
hand saw I was given is 1. dull and 2. unsuitable
for the stuff I'm cutting.

I've seen mention of some Stanley JetCut saw. Will
one of these live through cutting up to 35 - 40
feet total?

Power tools are out for vs. reasons. Also it felt
good doing it, even with the old dull saw.