I would not use those ganged component boxes. They are nice and handy, but if you drop a part when picking it up and it falls into the adjacent box, you are screwed... particularly with caps that are not marked. Opening and closing the lids when switching between parts helps, but can slow you down. On some the lids do not totally seal the compartment and parts can sneak under the lid into the adjacent one. Also on a lot of them the lids / hinges / snaps tend to break.
I use "medicine cups" and mark the part value on the side with a marker pen.