I'm going to make a small crane myself. The 2KW two-phase vertical test motor is equipped with a gearbox. What transmission ratio is used, or how many teeth are used?

In view of the limited data you provided, I can only tell you that the gearbox you chose is not a gear gearbox, but a worm gearbox. This gearbox has many transmission ratios, such as 1: 10, 1: 20 ...................................................................................... For a 2 kW motor, at least 1.5m (modulus) should be selected.