Pallets could work great for the storage. You just have to be creative about designing the stuff you want in your house. I had an issue of storage in my bathroom where I wanted my bathroom stuff to be covered and not just scattered in the bathroom so I and my husband decided to make a storage area in the bathroom made of pallets.
We made shelves out of pallets to keep extra towels, tissue rolls, shampoos and other necessary stuff which we use in the bathroom. I wanted it to be separately covered which makes the bathroom looks clean and tidy. The shelves made of pallets would keep the things organized and clean behind the closed door of the cabinet we have made out of pallets for the bathroom. If you are worried about the storage in the bathroom then pallets would be the best to get started with and make a cabinet by your own self.