[DonRotolo]

Pulley inertia can be ignored. Really small ones have to rotate faster, and friction increases a little. Big ones rotate slower, reducing friction effects.

In general, for most pulleys, you pick the size based on purely mechanical considerations: Does it fit the mechanism well. For an elevator, something in the 1 to 4 inch range (depending on the size of the elevator structure members) would probably be about right.

Unlike gears and sprockets, the size of pulleys used for an elevator system (those that are not being driven by a motor at least) doesn't matter much.