Note that these are three independent, dependable sources of light. You should be able to exit the cave with any one of them. Every caver recognizes the fact that caves have uneven walls, ceilings and floors. You will hit your head at some point during a trip. Any helmet should also have a chin strap in order to keep the helmet on your head in the event of a fall.
Boots are always preferred to sneakers.
Dress in layers so that you can adjust for comfort. Gloves and kneepads are recommended. Take some with you to the cave. Small pack To carry your gear in the cave. It should have good closure so that things don't fall out, and should be rather durable.