The OWI Robotic Edge Arm is a cheap and terrific 5-degree-of-freedom robotic arm that just costs $37. It’s a great kit to build with a kid and won’t take more than a couple hours to finish. Out of the box, it can only be controlled manually with a remote control. You can buy a USB control interface for it, but it’s a waste of $27. It just lets you add a series of timed moves, but it’s not really scriptable, you can’t have it loop and because it just uses timing, there’s no reliable repeatability.
What you want is real computer control, with closed-loop feedback for precision. Good news: it’s super easy to connect an Arduino board to the OWI arm and let it do all the work! You won’t even have to take the OWI arm apart or damage it.