Hi for my basement shop project, I used mold/mildew resistant drywall, which is basically layered one side only in fiberglass instead of paper. I uses no paper. The other side is just the drywall without anything (the side towards the inside of the wall). This is good stuff, only about a dollar or two more a sheet for me, and well worth it. Be sure to also use paint that is mold resistant too as some are better than others. I'll not ever use paper faced drywall again after using this. Much better stuff.
An alternative would also be unfaced drywall with just the gypsum present. Gypsum is "mold free", it is the paper that is not if present. But the fiberglass or paper layer makes it look better when painted, or just give it two coats naked which would be fine too and mold free. - Paul