Potatoes need to be kept in a dry, cool, and dark place in order to stay fresh. Potatoes do not do well in the refrigerator, though, as temperatures that are too cold (below 50 degrees) will cause the starch in the potato to convert to sugar. That conversion will make the potatoes taste overly sweet, and will discolor them too.
Like potatoes, onions can be a little sensitive. They need to be stored in dry, dark, cool places, but they also need reasonable air circulation to stay fresh. On top of this, they should not be stored near potatoes, even though both foods need to be stored in similar conditions. Onions and potatoes bring out moisture and gasses in each other, causing them both to ripen faster. Refrigeration is a good choice to keep onions fresh. (Bonus: You’ll also tear less when you chop them!)
If you’ve purchased fresh meat from the store, feel free to keep it in its store wrapping and follow instructions as given. Re-wrapping and storing meat actually increases the risk of exposing it to bacteria along the way, so it’s best to trust the packaging on this one. If your meat didn’t come with a tray under it, though, put a plate underneath the package to catch any excess moisture. Find out how long meat really lasts in the fridge.