Caving, not so surprisingly, requires a helmet and light. These lights are specialised for caving and are completely waterproof. We do not recommend you bring your own light.
An undersuit is similar to that of a onsie. It is a fury layer designed to keep you warm. Note though that it is made of a special material (unlike a onsie) that does not stick to your skin when wet, keeping you warm whatever the terrain.
This is your waterproof layer. This will keep a lot of the water off of you and provides an extra layer of protection to your skin
These can be whatever wellies you want. Yes, including duck wellies.