If you think that toothpaste is a good idea to clean Jewelry, well it’s not. Yes, it removes tarnish tarnish from silver; it will wear down the metal and will mark to metal and stones. It can also harden underneath gemstones and it is hard also to remove it.
Dish soap is the number one strongest thing to use in Jewelry so never use it for your Jewelry. The denatured alcohol can be a good idea but say no for this if you will use it to pearls, opals, or emeralds because these stones are so soft.
Don’t use lemon juice or any acids because it can only damage delicate pieces.