If you have the facilities to laser cut aluminum, I would make a mount for the camera that includes support along the rotation axes. That way the motors you use can be smaller and only be in charge of pushing the camera instead of doing any real weight support. Like imagine a chicken on a spit or the Price is Right wheel, the weight is supported, and doesn't take much to rotate.
I'd stick with stepper motors, counting steps will work just fine if you're halfway decent with math.
Servos have limited range, and the continuous ones are harder to work with as you're writing speed and direction to them.
This project will have plenty of room for simple limit switches which will work just dandy wit stepper motors.