Relay or Transistor, your choice. Relay has the advantage of 0 voltage loss across the contacts. Transistor has the advantage of being able to use Arduino PWM output for speed control.
That relay module looks good - it uses the transistor output of the optpcoupler to turn on the relay. Arduino drives an LED in the optocoupler to control the transistor output.
Looks like it might have current limit resistors for the optocoupler LEDs already too, all you need to do is drive the input pin low. Be sure to connect Gnd to Arduino Gnd.
Blink without delay style coding will allow you to turn the fans off & on at different times.
There are also timer libraries to support that.