How long is it safe to store new tires before they degrade in quality?
It depends on the storage conditions. If kept at room temperature, not excessively humid or dry, and kept in the dark, they can be stored for a long time. Oftentimes for years. 

Your best storage bet is to wrap them in plastic and stash them in the back of a closet. I've kept high-end tubulars for two years that way and that rubber is much more sensitive to storage/dry rot compared to puncture-resistant tires.