Only hunted with bolt guns (recently) and with a lever gun (long ago)and I follow the list below:
Mag full, chamber empty, safety on (When setting out on the hunt: verify chamber empty, lock the bolt, safety on, load mag).
If I fired a shot, and I'm not ready to shoot again, I leave the empty case in the chamber and don't cycle the gun.
If hunting in a group, one person is designated "RSO" and verifies everyone following the above.
Mag full, chamber empty, safety on (When setting out on the hunt: verify chamber empty, lock the bolt, safety on, load mag).
If I fired a shot, and I'm not ready to shoot again, I leave the empty case in the chamber and don't cycle the gun.
If hunting in a group, one person is designated "RSO" and verifies everyone following the above.