I decided to keep Arduino board with the supporting circuitry, LCD module, stepper motor control module, buttons, LED-s etc. in a separate case (which I call 'controller housing') from the 110V relay for obvious reasons - safety.
The other identical case will house the receptacle/110V socket for the aquarium's light and the relay (power housing). The power cord with the plug will go out of the case to the 110V socket and the receptacle mounted on the case will provide relay controlled/scheduled from Arduino power source for the fish tank light (see the pictures at the end of this article).
From the controller housing, two wires will go to the power housing that will provide current for the relay's coil. This way the electronics part will be completely isolated from the high-voltage part (unless I screw up insulation inside the power housing, hopefully not). Another 4-wire connector will go from the controller housing to the feeding drum (stepper motor). I still need to drill some more holes for Arduino's power/USB sockets, LED-s, perhaps I will add a reset button to the controller housing.
Considering the (poor) level of my manual skills, this looks quite OK, judge for yourself.
Thank you for your time.