I live in an outer suburban/rural location with woods, fields, and wetlands close by. Wildlife including possums are in the area but I've never seen any sign of them bothering my compost bins. Yard waste, tree trimmings, eggshells, paper towels, veggie trimmings, and grass clippings don't hold much appeal - I've never seen 'coons or skunks, either. Occasionally, I've seen crows picking at the pile but they don't find much of interest so don't hang around. Actually, I take a live and let live attitude toward wildlife anyway; if a possum checks out my pile once in awhile, I don't care. He's not doing any harm. People get all worked up over wildlife and bugs for no reason most of the time; I think it's a general symptom of a society afflicted with nature deficit disorder.
Most omnivores (wild or domesticated) would be looking for animal protein but I never include meat scraps, bones, grease or dairy so there's no smell, no flies, no critters. Herbivores have no interest in decaying plant material so they're not interested either.
I'm a very casual composter. This property doesn't generate enough waste at any one time for me to build a "hot" compost pile, so I just pile stuff up and let nature do its thing. My compost bins are made from pallets, lined with scrap chicken wire, leveled and held together with a few screws and nails. Essentially free. I never turn my pile, but when I want the finished compost at the bottom, I take the top rough stuff off and pile it in the bin beside it. Right now I have two bins but want to add a third one to the pair. I will be building some easily removed front panels out of more scrap wood and chicken wire just to contain the stuff more neatly.