This said, I will be making an automated system based on a stepper motor. Note that normally these motors make 200 or 400 steps per full turn, which is not always enough. Microstepping, gears, or a belt drive can be used to make smaller steps. I will try a geared system. Gears don't have the best of reputations for the extra play that comes into the system. But I think (or hope...) that that won't be a problem as long as the moter is used one way.
Note that the hardware is only part of the job: you'll also have to write software for the controller. If you don't feel easy
I would start with 200/400 steps/turn, on my microscope that means 2 or 1 micrometers/step, respectively.
Software is (IMO) easier done that hardware, not many commands are needed, but the initial position of the moving part ("zero point") must be defined, so a "reset" will always bring the stage back to the starting point.
And, of course, provided that the communication protocol with the camera is available... actually of this I doubt...