Jessel,
Almost any motor will do. Stepper great for positioning. Requires knowledge.
Servo excellent in positioning,speed and power. Also Requires knowledge
Straight DC motor with shaft encoder used in closed loop replicating a Servo motor,would also work. Also, it too, requires knowledge of motor and engineering.
Like RonH said, you need to give at least some information as to what you know in motion and automation controls. Projects like yours are not done in one day.
Be more specific, as to the distance or length of object being moved, the mass being moved, and how many times it will do this per hr. All this has to be considered.
Good Luck.