Cash: bring ¥500-¥650 in cash from March-November, ¥350-¥450 from December-February. This should cover your entry ticket, cable cars, and water and snacks on the mountain
Backpack: to carry water, snacks, etc.
Water: the shortest route takes around 6 hours, and the longest 1-day route can take 13 hours, so make sure you bring a large bottle of water. You can also buy water on the mountain but they're expensive
Snacks and food: you can buy them inside but they're expensive. Better to pack your own snacks and food from outside.
Waterproof jacket: the temperature up in the mountain is about 10C lower than the base, and it can rain from time to time. So pack it just in case