Choosing proper motor type

Hi,
I am looking for a motor that will be used to open and close a screen door (36 in. travel)within 2-3 seconds (will be controlled with Arduino and any required sensor). I have tested that a weight of approx. 2kg (5 pounds) is required to move the door (tested with a pulley and cord).
My problem is that I do not know what type of motor to use: stepper motor, gearmotor, Servo, DC motor …
I have calculated that with a 2 inch diameter pulley, I need 6 full turns to open/close the door.
Can anyone suggest a type of motor and a capacity sufficient for this task ? I have no power constraints, as I will use a DC power supply of sufficient capacity.
Thanks,

Consider a linear actuator at a pulley system.
Since we don’t carry any linear actuators which can travel at 12 to 18"/s, you can add pulleys to reduce the travel needed, but consequently increase the force required.
As such, you can probably get away with using a shorter stroke, but higher force linear actuator.
Unfortunately we don’t have a variety of pulleys for you to create the system, but you should be able to find them online.