Apart from the deep ocean, caves represent parts of the Earth that are still unexplored. Ok, I haven't been in any unexplored caves yet, but even in mapped caves you get the feeling that you are on a great exploration adventure. It is a really cool feeling to crawl through mud, squeeze through tight tunnels and suddenly pop up into a huge chamber, decorated with stalagmites, completely quiet except perhaps for dripping water. Absolute essentials are a Helmet and a Head torch. See my brother's reply.
Essential equipment is definitely a helmet and a head torch.
In principle, you can go naked with these two bits of gear. A little bit extreme perhaps. I guess not. I do a lot of rock climbing as well. No I have been climbing and caving and doing other silly things for ages, but heights have never really bothered me.