I see your threads are Connecting Threads, same as mine. I bought a rolling 5-drawer cart to keep mine in by color. They can sit upright too..........until recently as CT has changed their spool to a taller one which has the color # on one end. Now they are too tall for the drawer. My embroidery threads are all on a pegboard and I keep old tea towels over them to keep the dust off as my sewing room is in the basement. I've ran out of room for my quilting (CT) thread so need to figure out a new system for them. I keep the larger cones from CT on a thread rack with plastic straws cut longer than the dowel pins to keep them from falling off. I thought about getting additional pegboard hooks but due to the curve on the end the new spools won't go thru completely.
But as to the 5 drawer cart, I keep the bobbins next to the thread it goes with. I cut the thread label and stick it inside the spool for reference.