Minecraft wiki entry for Exploring_an_ancient_city, associated text: A safe escape route, so that you can leave as fast as possible if things go wrong.
You could also build a fortified and closed-off "panic room" that you can flee into and take cover inside.
Food, to keep you sustained.
Light sources, like Torches (but be careful about placing them, as detailed below)
Tools and Weapons to both maneuver your way around and deal with potential hostile mobs (but not the Warden)
Armor to keep you safe.
Patience, as you will need to sneak for almost the entirety of you journey through the Ancient City.
You could also change the settings to make sneaking an on-toggle action, instead of having to continuously hold down the sneak key.