Chuck Norris.
But seriously, I agree with Timmundo's suggestion about Journey- its a nice read and a good foundation for this kind of adventure.
The party should have your typical stuff for a dungeon crawl.
1) Magical and mundane light and fire sources.
2) Provisions and/or someone who knows how to forage in the Underdark and/or a magical food supply.
3) Rope, rope, and more rope. And to go with it, rope. In addition, carryi all the spelunking gear you'd need- pitons and the like.
4) A way to restock spent missiles. Easy: everyone carries a sling. Hard: everyone carries a bow & arrow, and uses a Quiver of Ehlonna for extra arrow & bowmaking supplies.
5) Depending on the "realism" of the campaign, a way to restock expended material components...or the Eschew Materials feat.
6) Staples: Ye Olde 10' Staff, The $1.25 quarterstaff, and the Universal Adjusting Tool (aka, a hammer), Poor Man's Key (Crowbar).
7) Caltrops and/or marbles, because there will definitely come a time when you will have to beat feet.