arduino hardware and software for a robotics device

I have a small project now and a bigger project coming soon. The small project includes a servo driven rack and pinion mechanism You can find the specifications on the page of the product: [login to view URL] I contacted their customer support and this is what they told me "A Servo motor needs a PWM (pulse width modulation) signal to rotate. This signal can be generated by a microcontroller or an Arduino. The Arduino Nano is small and can output up to 6 PWM signal: [login to view URL] Concerning the required voltage, you would need something around 4.8V and 6V but we would recommend 6V so you could power up the motor and the Arduino with the same power supply." I need your help with exact instructions: what parts to purchase, how to connect, how to operate. The big project will operate six rack and pinion mechanisms (same as above) using specific logic related to either a program or sensors or combined. Also will include a linear actuator, a large stepper motor, and few more items. Basically it will be a full circuit and program to operate the device shown in this video: [login to view URL]