The height has nothing to do with the selection of the motor.
Whichever motor type you choose (servo or step motors will allow you control the exact position while simple induction motor just cannot) - you should verify it has sufficient torque capabilities for the desired lifting velocity.
The needed torque in your case is calculated as follows:
1. for a constant speed: the load mass * g * the distance of the weight from the motor axis center (in meters)
2. for accelerating lifting: the load mass * the linear acceleration (in m/t^2) * the distance of the weight from the motor axis center (in meters)
the results for both cases are in Nm units.
Next, you need to convert the desired lift speed to the motor angular velocity. Basically, all you need to do is to divide to linear speed (m/sec) by pulley radius (m) to have it in rad/sec.
Each motor has a specific torque-speed curve. You should make sure your motor can supply the needed torque for the desired speed.
Furthermore, you should relate to the motor peak torque only when this torque is applied for a short period of time. Otherwise, the motor will heat-up and wouldn't be able to supply enough torque.