What speeds are you imagining?
What mark said about 45RPM seems about right to me. I don't want it spinning so fast that the arms are parallel to the ground, which I assume would happen before things started flying off.
Torque isn't important for the arms to raise (assuming low friction), only angular velocity. To get up to speed quickly you do
need more torque - so how quickly do you want to change angular velocity?
I think 0-45PM in 3-5 seconds is about what I'm aiming for. I'm quite certain I will screw this up somehow so I am assuming I may try more than one motor. So my Arduino will send a PWM signal to the motor shield, and that controls the speed of the motor?
For my purposes, a geared motor just means more torque, right?
Are there any retailers you'd recommend for parts like this? The amount of specifications given for little DC motors seem all over the place.