The obvious weapon for a dungeon crawler is a pike. It combines long reach and thrusting action (because you'll often have limited space preventing you from taking a swing); a pike is perfect for holding back a monster in a narrow tunnel.
Your sidearm would be a short sword, something to use at close quarters when a foe gets past the pointy stick. It would probably acquire some morbid slang name, because if a monster is close enough that you need the short sword, your odds of survival are... not good.
Crossbows would be the ranged weapon of choice. Again, they work better in tight spaces than other ranged weapons, and pack a lot of punch for Large-sized foes.
I can't see either a rapier or a broadsword getting much use. It's not that they're bad weapons, they're just designed for very different forms of combat.