The circuit should be something like the figure attached.
Not really, because the load's on the wrong side of the NPN transistor 8)
You should consider limit switches too: "bump" switches at the top and bottom of the travel to make sure it switches off and doesn't sit forever trying to grind its way through the end of the system.
The mechanical side of this project might be tricky: how are you going to get the motor to move the platform?- usual approach is some kind of travelling nut on a threaded rod, rod turned by the motor.
Edit: something like this...