For my spools that do not have a snap bottom, I bought some lightweight clear plastic at Joann's and cut strips the width of the spools, then I cut the strips so that they wrapped around the spool with about 1" overlap. (I did start with a paper pattern) The plastic sticks to itself and the thread stays neat.
I store the thread I use for piecing in a handy drawer, the specialty threads are in plastic boxes sorted by type (like metalic, poly, cotton, varigated, 30 wt and 12 wt).