I am building a pole camera, normally you would have someone on the other end to move the pole, but we want to be able to operate it remotely. As the movement needs to be very smooth, with a soft start and soft finish, some sort of dampening needs to be added into the pole motor movement. The pole itself will be about 2.8 meters long, with a lightweight HD PTZ camera at the end. I'd like to be able to have control over the current position of of the pole, no need for tilt, only for pan, as well as setting presets, and auto move. Auto move would be something like setting limits to the pan, and having the pole move in a sin wave side to side. I'm thinking something like an arduino for the control, but uncertain of what would be good mechanically to move the pole not only with precision, but also be very strong, as we often get very high winds.
A PID controller may be more then what you need, but a PID controller can control the damping and overshoot of your motor. There is more on PID controllers at How to learn PID Control?
As for your motors, I think using a stepper motor will probably be your best option. There is some information about stepper motors at Arduino Stepper Motor
Using an Arduino or any other micro-controller should work just fine for you.