Unless they're aerosolized (e.g. by sneezing), or specifically designed to do so (like mold spores), food contaminants are very rarely airborne. All of your food comes with its share of bacteria, so the goal of the fridge is not to keep things sterile, but to greatly slow the growth of these organisms.
As mentioned above, the biggest thing you can do is keep your fridge clean, and put things away in such a way that things such as meat juices (where meat must be cooked to be safe) do not drip on things like salad greens, which may be consumed raw.
Plastic bags are great for some things (such as containing a drippy container of meat), but they will trap moisture around fruits and vegetables, leading to earlier wilting and spoilage. Better than plastic bags would be simple tubs (tupperware, glad, anything). Put different types of ingredients in their own tubs (wash regularly), keep fruits and vegetables in the open air in these tubs, but keep the wrapper on meat and cheese. This should contain any spill that could happen.
As for the air, unless you have something actively growing large mold which gets disturbed, there is little the air can carry that would contaminate your food. It may smell, and that smell may permeate some foods, but will not cause contaminations.