Suggestions on finishing a concrete vault
A hundred years ago, that would be called a 'root cellar', and considered a great place to keep your potato crop or smoked meats.  The temperature will be relatively constant down there because of the ground contact.  Insulating will actually reduce that thermal buffering effect given the vents.

Your problem for guns and art is humidity.  I'd start by measuring the humidity to see where you stand.  A USB hygrometer is an inexpensive tool for plotting humidity over time, and you'll want that even if you go all modern and try to seal the room.