Your description is very rough, so don't expect much help. You should let us know what You've done so far. Dimensions of the car and balls. Current design that You want to implement. Etc...
You should give us specific questions like: "How much torque do I need to lift 10kg ball with 10cm length arm?" and not: "How to build robot that can do this and that?", there are plenty tutorials on how to build robots, robotic arms, program microcontrollers, use sensors, etc.
To answer Your question - yes, steppers are very useful when building robotic arms.