This low power, low speed stepper motor costs very little and is used in some of the later videos. Make sure you get it with the ULN2003 controller board as it means less load on the ATmega's output pins. The motor has 28BYJ-48 written on its back.
Here's one way to hook the controller board to the Arduino (we're using pins 2, 4, 5 and 6 because they go through to the ThinkerShield's alligator clip points): The board has pins rather than sockets, so your hookup wires will need to have female connectors at that that end. The jumper on the board controls whether an LED comes on with each phase of the motor.