I keep all my organs/fat/muscle uncovered at around 32-35 degrees Fahrenheit/0-2 degrees Celsius, placed on some butcher paper.
I would suggest keeping it uncovered unless you are trying to make high meat. In the past, I've had meat at somewhat higher temperatures stored in plastic for over a week, after which it would gain a vile bitter taste. If you do plan on keeping it in sealed jars, I suggest airing it regularly. Since your problem seems to be your housemates, keeping it uncovered would be fine.