Ground? Where?

[IotaYodi]

I finally am truly asking what I consider an important question, so any ideas, either way, would be appreciated.  It's even on topic.  Where should this ground be attached?  (To those who know the code well, is it possible that there is a code that states a dryer powered from a secondary panel requires altering to a 4 wire plug?

The 3 wire for dryers is from the older code. 4 wire is in newer installations. If the sub panel is new then 4 wire is needed. The 4 wire is added safety. The ground wire is attached to the chassis.
Wire size is matched to the load and breaker rating. There is a max and min for current carrying wires as well as the ground. A breaker uses circuit impedance to limit the actual peak currents to where it trips the breaker. If the wire is too large the impedance goes down and possibly wont trip the breaker. Heating will then occur and can cause fires.