Broken spoke needs replacing and need a few spares.

Is it the distance between the thread and the end?

The bend to the spoke end inc' the thread ... so just measure the entire straight part of the spoke.

A couple of my factory made wheels have a sticker on the rim telling me what length they are

I also back in my student days needed a new wheel for my campus bike. I got hold off a friend a mavic cxp33 rim for the cost of a pint of beer, and got a DH 32H hub off eBay for £8. I then got hold of the cheapest spokes possible to build it - unfortunately due to the lengths I had to splash out on DT swiss spokes for one side. Anyway, built the wheel - all fine considering. However the side with the cheaper spokes had to keep on being done up every couple of months, the DT swiss side were fine throughout