Even though I reckon the wall hanger thing above absolutely rules

It's currently
"..transparent storage boxes, and transparent zipper pouches" for me
Easy to store and travel to jobs with (what do I need?

meh take the lot..)
and most important reduces the chances for dust and crust settling on the connectors when sitting there 24/7
FWIW in use I'll use chairs, step ladder or stretched out bungy cord or plastic conduit as a poor mans temp wall hanger
and any lead set that belongs to a meter, stays with that meter,
not always a hard rule if the leads are nice to use

EDIT: what would be nice, and tick most boxes for me, is to double back/loop the leads on the wall hanger,
and have a flap or some sort of easy cover when not in use = less dust and crust
This way the leads are always clean, fresh and 'conductive', a great help and no brainer on hurried low level probing