Police shotguns have been carried in variations of "cruiser ready" for probably a century now. Many decades anyway. Although you will read of different versions of hammer cocked or hammer down, and safety on or safety off, the one thing that always remains the same seems to be a fully loaded magazine tube.
I stow mine with empty chamber, full magazine(5). I prefer hammer cocked because this means the forearm is locked forward in a positive, secure position for a fast grab if needed. Safety on.