Here's a hint for handling those dripping meat packages at the grocery store. Take one of those plastic produce or meat bags and use it as a glove before you pick up and bag your meat or poultry.
I usually save the bag to put the wrap, fat and other trimmings into and tie it up before it goes into the trash. Sometimes, I'll put them in the bag, then in a used ziplock.
Those same types of bags are used by athletic trainers to put ice into. Why, I don't know, because they always leak.