which motor for arm?

[JessR]

Two principles to keep in mind are to make the weight at the end of your arm as light as possible, and to balance the weight of the arm with a spring of some kind. This will allow you to use the motors' power only to move the arm and lift the weight of the playing piece (this year the inflatable rings).
Examples:
If the arm only rotates 90 degrees you could use a gas strut (similar to what holds up the rear hatch of hatchback cars) or compression spring to balance some of the weight. In the USA gas struts are available in auto parts stores.
You could also use surgical rubber tubing that passes around a narrow, large diameter pulley at the arm axle and is attached to the chassis below.
To keep the arm parked in a specific location, From a control standpoint - you could mount a potentiometer or encoder on the arm axle and use a "PID control loop" software to have the software drive the motor to keep the arm positioned as the last potentiometer or encoder location when you took your hands off the joystick or 'on' button.