Assuming you are going to start with stepper motors they need a suitable driver board. The driver board takes instructions from the Arduino and power from a power supply and sends suitable power pulses to the coils in the stepper motor. You need to match the driver and the motor.
You will probably want physically small stepper motors - perhaps something like this or this. These are bipolar stepper motors and can be driven with a stepper motor driver board (one for each motor) like this or its Pololu equivalent.
And no matter what the project in your video uses, start simple without encoders.
...R