noahwass:
Just so I am clear, you're stating that I do not need limit switches
You do need at least one limit switch so the stepper motor can find the zero position and I would put a limit switch at the top and bottom.
If you have a limit switch at the top and bottom a simple DC motor with low gearing would work, and would probably be better. If it uses a worm drive the elevator won't move when the motor is unpowered, Stepper motors draw full power all of the time, even when stationary.
...R
Stepper Motor Basics
Simple Stepper Code
also look up the AccelStepper library