I have thread stashed everywhere!
At the machine, are the spools that have been started.
Left drawer has polyesters. Right drawer has cottons.
Bobbins are held onto the matching thread, with a bobbin buddy/stick.
Away from the machine is my stash of new spools, again separate drawers according to type of thread.
I have several of the fancier embroidery type threads that I use for FMQing or straight-line quilting. Because they are not used regularly, the started ones are kept at the front of the drawer and the others behind a divider.
Over the years I have had different ways of storing my threads.
This is what is working well for me now.
There is no "right" way, as a lot depends on what space you have available for thread storage ... and how much thread you keep in your stash!