If your rescue team is defeated in the dungeon, you lose all the items and money you had with you. But your items in the storage and money in the bank will be safe. Therefore you should store your items and deposit your money before going for a quest in the dungeon.
Storing your items will also create space in your toolbox which can be useful for picking up items that you discover in the dungeon. Carry only few important items into the dungeon like apples, potions, and orbs etc. as per your needs.
Deposit your money in the Felicity Bank. Carry only a small amount for buying items from the dungeon shop and for making rescue camps from the dungeon.