I can weight in on supplement storage since this used to be my old line of work.

Any changes in temp and humidity will start the degradation process on your supplement products. This is called deliquescense. B vitamins are particularly sensitive with Vitamin C being the most sensitive of all. Oxygen and light exposure will degrade these vitamins as well.

Don't store your supplements in the refrigerate unless the bottle tells you to do that, however you can put them in the fridge for long term storage if you are not going to use them. Make sure everything is sealed up and in a brown bottle so you avoid light and oxygen damage.

The supplements that you are actively using, store in a cool and dry place (unless otherwise specified). Make sure the container is tightly sealed and that they are in a container that keeps them shielded from light.

Also, bathrooms and kitchens make for poor places to store your supplements and pharmaceuticals since they vary the most in humidity and temperature.