I think that no matter what type of motor you choose, you will need to build a feedback system for precise positioning of the motor (unless of course you choose a motor that already has this feature ie. servo motor).
As you have already said, if you used a DC motor, you would need to build a gearbox.
All things considered I would reccommend you use the servo motors. Although these may be more expensive, I think the few dollars more that you spend will become worth it when you relise the simplicity of installing a servo motor.