You could work out a formula as the number of teeth x pitch will equal the circumference of the pulley however to be honest, you would be better dividing the teeth on the large pulley by the teeth on the small pulley and that's your ratio.

You will almost certainly need a two stage reduction if you are using timing belts based on the available pulley sizes. Your other issue is that the pulleys are generally made from steel and the large ones weigh a hell of a lot.

To be honest, I'd look towards a chain driven system. It will withstand a bit of misalignment, take up less space, the cogs are likely to be lighter and you can make a custom length of chain. Gearboxes can be wonderful but custom ones require access to a milling machine to get the required tolerances to allow the gears to mesh properly. Mind you if you know someone with a mill this can be a good route for a dependable system.

Technobots would be my go to for chain / sprockets and gears http://www.technobotsonline.com/spro...and-chain.html

Not sure if there's anywhere better these days. Check out the 0.375" chain. The 0.5" can be used and I have done in the past with a heavyweight but it's really overkill.