Sorry knut_ny but SSR means Solid State Relay and they can be for both DC ar AC drivers and the one you show is DC. You just need to choose the one you need as they are not alternatives or swappable.
I do not think you can use one of this for the Ground. For DC it is not so critical leaving the ground connected.
Anyway the PCB you show has everything the arduino needs, do not need any more resistor nor any other.
Regards