Hmm, you've gotten me interested now, so I might need to do some further research into cave formation...
Based on a very quick Google search, the most common type of cave, and the largest cave systems, are formed when water flows through groundrock, most commonly limestone. Water naturally takes the path of least resistance, which means it follows existing faults and cracks. Over time, the continual flow of the water will enlarge those cracks, and eventually hollow out larger chambers.
From the point of view of making a map of all of this, having a natural cave system that twists all over the place like spaghetti is actually unlikely. Geology doesn't tend to work that way. It might be helpful to think of geological faults like a broken glass window: the cracks in a window aren't random, but run parallel to each other, varying in width, distance and depth.
I've scanned Google images to find some reasonably good real-world cave maps for you:
Oregon caves: does a good job of showing the way caves have many passages, but remain mostly linear
Laurel Caverns: shows the geological structure of the faults in the almost grid-like corridors on the left
Glowworm Cave: this example from your own country, shows that all of the cracks seem to be aligned in a particular direction (i.e. running from SW --> NE)
One problem that I think exists in all of these examples is that they don't really give a sense of what the interior of the cave is like. From my limited experience of caving, I know that caves go up, down, in, out, under, over; sometimes they have giant caverns, and sometimes they have tiny fissures that a person can barely squeeze through; sometimes the ceiling is almost out of sight above you, and other times it's so low you have to crawl; and sometimes the floor is smooth, sometimes it is rough and bumpy, and sometimes it's completely flooded. Doing both a plan and a side view might help you capture some of that claustrophobia (and grandeur).
Hope that's helpful. Remember, I am certainly no expert on caves, so I might be wrong about a lot of this.
Wingshaw