How many headset spacers might I need? I am building a bike. The headset is in the head tube, and the next thing is to fit the stem and handlebar to the steerer. At this point, it seems I need some headset spacers in between the headset and the stem.

How many headset spacers am I likely to need? Or rather, how much total height of spacers? Is there any way to work this out other than trial and error?

The frame has quite different geometry to my current frame, although my body's geometry is not changing. Should I try to reproduce the space on my current bike?

Headset spacers are available in all sorts of combinations; would it be prudent to get something like a pack of five 10 mm spacers? Or a set of a 10 mm and two 5 mm? Am I likely to need more space than that? Less?
You can get a close approximation if you have access to a trainer. Install the bike in the trainer with the fork and headset installed. Using a front wheel riser block will make the fit closer to your actual riding position. You can now install the stem at any height you like. When you find something close measure the gap between the bottom of the stem and the top of the headset. I would get a variety set. Most come with a 2mm,5mm,10mm and 20mm. I just did this myself and I got an extra 20mm that I installed above the stem.This allows for some flexibility later. The spacers can be shifted for a different fit for different riders or resale. It is easier to cut the steerer later than try to make it longer.