I generally use waxed paper — as it breathes a bit more than the others.
The inexpensive ($10) yellow-plastic Hutzler Cheese Saver is worth a try, especially if you’re a cheese lover, like me.
I found that for the most part, my cheeses stayed fresh longer, as it also allows them to breathe.
To use it, place a moist paper towel beneath the perforated plastic shelf and put the cheese on it. The cheese does stay fresh longer, whether hard or soft.