An RC servo converted to continuous rotation would be what I'd recommend. That would give you gear reduction, the motor driver, and a simple interface. The sweep
tutorial gives an example of how to code for one, but in the case of a continuous motion servo turning the potentiometer farther results in the servo spinning faster ... which sounds like what you want.
You would use a stepper motor only if you wanted to be able to programmatically determine the position of the claw (e.g. "move exactly 10 centimeters"). In your case you have a operator at the joystick and don't really care where the claw moves -- just that the operator can move it.
Timing pulley that fits servos: http://www.lynxmotion.com/p-332-hitec-servo-mxl-timing-belt-pulley-32-tooth.aspx
Makerslide would make a good rail system: http://www.ulule.com/makerslide/
Converting servos to continuous rotation: http://www.societyofrobots.com/actuators_modifyservo.shtml