Lets see... Currently it's steel armor, (with helm of minor archery) Dwarven bow, silver longsword (for the undead) 2-handed Nord sword, one-handed axe of cold.... Oh, wait... That's Skyrim.
 
Really, why would I want to descend into a dungeon?   They tend to smell bad and be filled with miserable prisoners and ill-tempered guards.
 
As to caves... Really cool.  I mean...COLD.  Also, wet and muddy, cramped, dark... Much nicer to watch those nice National Geographic specials.
Did I mention the bat guano?

Mmmmm... American Graffiti?
Lascaux Graffiti?
Can't remember the title....  
Greetings,
Mauro.

hm...
with benefit of what y'all picked, here are my selections:
 
warm clothing, leather gloves, a hardhat, good boots, a good headlamp(and lots of batteries), safety glasses and earmuffs(for zombie gore),
lye spritzer in case oozes are acidic, an emergency blanket and extra sweaters, clif bars, water, a first aid kit, rope, a good knife, electric canary & oxygen tank
plus, a zombie hammer, a weapon of my own design consisting more or less of a framing hammer with an elongated, pointed head with a small axe where the claw would be.
ooh, almost
 
i would also take, as a companion, either:
Morgon of Hed, The Rowan(or any other Prime, but preferably a member of her family), or the Deryni Alaric.
 
Morgon would be best, but any of them could help locate Ulrica's kids, and be extremely useful in a fight.
Alaric could help if they were injured, but the others would be better for transport and fights, thus is at the bottom of the list