EMP is a highly debatable and controversial subject. Your device survivability will greatly depend on pulse intensity, rise time, location, orientation, external connections etc.
A Faraday Cage is rated by it's attenuation to a defined range of RF frequencies. I would advice to use a Faraday Cage with at least 50 db. of attenuation for guaranteed protection at high intensity levels. From what I've learned, measurements are done in the 300 to 700 Mhz range for checking EMP shielding.
A steel ammo can offers very little attenuation because of the gap between the case and the lid. Same with a metal trash can with a metal lid. The gaps in the lid will act as a slot antenna thus allowing a lot of RF to get inside.
You should use an aluminum duct tape to continuously seal all the gaps.
For ammo cans, use a sheet of aluminum foil, slightly larger than the can opening. Lay it over the opening and then close the lid on top of it. This will greatly boost RF attenuation to nearly acceptable levels.
Metal buildings offer very little attenuation, especially if there are doors, windows, large gaps.
Grounding a Faraday Cage does almost nothing to it's protection ratings. Actually, long grounding conductors may only make things worse.
You can purchase conductive cloth and make bags or vehicle covers from it. It's not cheap but it works. For a vehicle cover, the fabric skirt must be on the ground for at least a foot, along the perimeter of the vehicle. Same with motorcycles, generators, solar panels (not installed) etc. If installed above ground, it must have a metal pan under it and the fabric must me touching the pan continuously along the perimeter.