For Meat claws, I highly recommend "Original Bear Paws", which are available for about $13 from Amazon. They make fast work of shredding. I can fully shred 2 pounds of meat in about 2 minutes. They also are great for lifting large roasts.
First safety I recommend you buy them in one of the BRIGHT colors, so you can easily see them in your utensil drawer.
Washing and drying -- they are dishwasher safe on the top rack. If you have to hand wash and dry them, I would hold them 'tines' downward and dry working top downward.
Storage -- I have mine pressed into dense, closed-cell foam, like expensive, heavy electronics come packaged in; pool noodles are made from this type of foam. Pressing them into the foam the first time kind of takes gorilla strength, but after that they go in fairly easily. You can make them easier to insert the first time by cutting an 'X' in the foam with a utility knife for each claw tine.