I store my thread in those little sets of drawers that are sold for keeping screws and nails in from the D-I-Y stores. If you are uncertain about which size you need, just slip a couple of your spools in your pocket and you can check in store which they fit.
For larger cones, they live in the second drawer down of the unit underneath.
Older natural fibre threads do rot, same as fabric. And different colour dyestuffs affect the same base fabric differently, which is why a blue fabric could have a different 'hand' to a yellow or red, this will also affect rate of deterioration.
I also have some very old Pearsall's silk floss thread, and the to tell if they are totally past it for using is if you can rotate the thread whilst holding onto the spool with the other hand, if you can't you are probably ok for careful hand sewing.
Rosemary