If you are planning to stockpile film or paper and hold it for years, you want a freezer (chest type, because they tend to be more efficient and over time the electricity cost adds up). If you just want to make sure that your stock doesn't degrade before you can use it, a refrigerator is fine, and you will not have to plan so far ahead when you want to bring something out and use it.

From experience, I would recommend sealing anything intended for freezer storage in an airtight package. Not that the air is an issue, but when the inevitable freezer failure, power loss, or accidental-door-left-ajar event comes along, melting frost and condensation will be kept away from the material. For anything that will fit, a vacuum/heat seal food packaging appliance is great. (I still haven't found a really good solution for 11x14 film and paper boxes, so maybe an industrial-size bag sealer is something to consider.)

Regarding chemicals (b/w only, in my case) I have never had a problem with degradation that wasn't connected to air exposure. The backyard darkroom gets into the Fahrenheit mid-90s on hot days, but I have to keep it warm during the winter lest I go out to work and find crystals in the bottoms of the Dektol and fixer bottles.