What type of stepper motor should I use in my project and how do I control them?
One important factor when working with stepper motors is hold torque. You can do some simple calculations based on your camera weight and platform radius to determine the torque due to gravity, and your hold torque should be a fair about larger than that or the motor will slip. 
You'll also need stepper motor drivers in order to control the motors and provide enough current as well as the proper signal to control the motor. I've had experience with the Pololu A4988 I'm conjunction with Arduino; it's simple to use and only used 2 digital IO pins (at minimum). You can also spare more pins and control things like the driver enable, etc. 
As for actually choosing a motor, that can be tough. I'd pick a price range and form factor that you'd like to be within and use that to narrow it down. I'd also stay away from the spark fun motors as they are usually on the more expensive end and not the best bang for the buck.