As for maps, caves are 3d, but a regular topo map should suffice. This is because there is a ceiling. It may be useful to know that cave x goes over cave y at this point, but unless they connect it mostly doesn't matter. A cave system may start at one elevation, and end at another, but its the connection points that really matter. Also, depending on your world, they may be constantly changing, beyond your controlled kingdom areas, due to rock worms, are whatever other borrowing creatures you have making new routes and collapsing old one. Even just geological activity could cause enough unrest to make maps unusable.
Also, from way back, look at the Death Gate Cycle's Fire Sea, third book in the series. Similar world. And a good series.