When I clean the fridge, I wipe thoroughly with those Clorox bleach wipes, rinse and dry to avoid mold. If you keep a lot of cheeses on hand, a paper towel soaked in vinegar will keep mold away; keep it separate from the cheese with plastic. I can't speak for bags of opened grated cheese, those I need to use up fairly quickly after opened but I keep mine in the meat drawer.
They are a little nuisance having to life the 4 flaps, but they work better than any sealed contained I ever had. Am going to get more for my freezer when I get it more emptied out and try to clean it.
I had my fridge sparkling and got rid of lots of stuff, always wipe the bottoms of some jars when I clean B4 putting them back in. It had gotten pretty bad though. I wiped it all down with bleach wipes after washing. The fridge temp is much better. I bought a container to put my milk in and a thermometer hangs on it. It has been keeping a lot longer.
Finally I use cottage cheese and similar lids to set the opened cat food on and my coffee I make and reheat for 2 more days. Also put plastic pans for bigger stuff also pizza pan for big kettles of things like soup.
Paper is a good idea, too, didn't think of that but maybe it's just easier for me to wipe and dry with a paper towel, spot clean. My shelves are glass, and it's tricky business getting them out and back in. I set the big ones on 4 cottage cheese lids on the counter to clean, then flipped to the other side. Now that I know how they fit in, it is a little easier.
Items are from amazon. First there are all difference sizes, individual and sets to choose from.
For the milk and other dairy, sorry it's so small, the one I wanted to post is too big and made the page scroll:
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