The other thing that client, designer both have to remember is that both vaults and storm shelters need a roof. That's a proper roof, and not merely the floor structure above.
hso's comment is germane here. Keeping the fire fighting water out is as important as ground moisture; it's also the only way to stay safe in an F-4 or F-5 tornadoe (which will strip floors from foundations, as was seen in Jarret).
This need not be complicated, a 1.5" "W" deck with 1.5" of concrete over that will suffice nicely--if the deck is tied to the walls.
As a storm shelter, you probably do not want to install a safe (or RSC) door. These would be too slow to get into, and be something of a hassle to exit through. Not a bad idea to have a second exit from a storm shelter, in case the first is blocked by debris.
To keep this on topic, let us now address guns and ammo. Resist any idea of placing either guns or ammo directly on the floor. Concrete passes moisture, slowly, but surely. Also, the issue of water, rain, storm, firefighting remains . You probably will want locking cabinets (of the Stak-On variety or the like) too, as a goldenrod or similar dehumidifier works better in confined spaces.
Alternately, since this is a "protected" space, one could keep the arms in glass fronted cases, if that suits the fit and finish of the space.
As to design, a tornado warning sledom lasts more than an hour, so you'll want seating for everyone you expect to shelter. Now, the time spent in a shelter is laregely one of listening to the weather radio, unless you care to make other entertainment options available.
This is important as, if you are finishing this space as a "gun room" with leather chairs and the like, that will warrant a different sort of fit and finish than a painted block wall with wooden benches for ammo and people sheltering for a time.
That's my 2¢, any much more and I'd have to bill you (and bet an AL license, too).