It is not clear whether you are trying to solve some specific problem, or whether you are asking generic questions about shielding and grounding?
You appear to be constructing your power/control circuits on a large metal plate. I would certainly connect that plate to the green-wire safety ground of the mains power supplying the unit. That would provide not only safety ground (in case of failure of any of the supply or control circuit elements), but it would also provide signal shielding when connected properly.
You don't necessarily need shielding on the output wiring going to the stepping motors, etc. But the controller may be sensitive to interference from transients caused by switching large power loads (i.e. feeding the stepping motors).
Generally, things with a separate ground terminal should be connected to the large metal plate that forms your "chassis".
It is common to find the controller (Arduino board or whatever) in a separate (and separately shielded) enclosure to protect it from transients. And it is also not unusual to see optical coupling used between the controller and the motor drivers. That decouples any large switching currents from possibly getting back into the controller.
But you may want to simply finish the construction and test the system to see you actually have a problem or not. With that nice big ground plane, you may not have a problem at all.