I bought a rolling 5 drawer metal toolbox to put all the lathe tooling I have in [my dad had all the bits in a variety of wood boxes, fishing tackle box, small metal toolbox, swarf pan under the lathe, and on/buried on any flat surface in the immediate vicinity of the lathe].
The 4-jaw chuck, lamppost holder [which I doubt I'll ever use, but you never know], the two lathe guides/supports are in the bottom drawer. But once I added the faceplate to the drawer, the whole thing started tipping over on me, just managed to keep the toolbox mostly upright and have not too much stuff roll off the top before getting the faceplate back out. Now it rests off to the side of the lathe.