My threads are stored in a Bernina thread box that I won years ago.
I have alot of thread so also have an Ace Hardware box that another student at QBL showed me - also holds wider spools than the Bernina.
Threads that are likely to be in current use are on a thread rack that hangs on the wall behind my machine.
Cones are on a cone-tree.
My bobbins are stored in drugstore daily pill boxes and in the rubber circle bobbin holders that I bought w/coupons at Joanns.
One color for cotton, another for Bottom Line.