Nothing ironic about it. As soon as you break the rind of a real cheese you've doomed it.
What type are you trying to store? It matters. Hard cheese will last longer than soft/paste cheeses.
Paraphrased from a number of sources and experience:
Bloomy rind cheeses: just cover the cut/exposed part with plastic... let the rind breath.
Washed rind cheese: cheese paper or wax paper. Anything greaseproof.
Blue cheese: tightly in foil.
Soft cheeses (ripe brie etc): cheese paper or wax paper. Again, anything greaseproof. Sealed containers also work in this specific case.
In general, any cheese that you can wrap in paper is best off in cheese paper; wax paper also works in a pinch. Keep it in what it came in, unless that was plastic. If it came in plastic, after you have opened it, wrap it in waxpaper/cheese paper. You need to let cheese breath.
Technically, the cheese should be checked re-wrapped daily but most people aren't going to go that far.
Keep the cheese in the bottom of the fridge where temps are most stable. If your refridgerator is aggressive in terms of being frost free or keeps the atmosphere inside quite dry, think about keeping it in the crisper intended for a little higher humidity. In general, the vegetable crisper is a great option. Don't freeze it.
Mold is going to grow and that's normal, it is a living food. If it is the same as is on the rind or in the blue, it's fine. You can cut, scrape or wipe it off. Anything more than 1/4", toss it. Slimy? Toss it.