A pillow case or snake bag would be fine for when you clean his cage, just make sure it is tied securely.
As for cleaning, I use a bleach/water. I used 9-10 parts water to 1 part bleach. If you go this route make sure you rinse it well. There are other things you can use, but this works best for me because I'm usually cleaning 10+ tubs at a time.
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