I keep mine in the box (and keep that in a leather pouch, in a drawer). I also
always swab the top with alcohol. And I try never to actually touch the top if at all avoidable.
Additionally, you'll need to be a bit more cautious with the MDV's as you can easily contaminate your vials if you're not paying due diligence to what you are doing.
Never, ever use even just a drawing needle more than once.
Never, ever use even just a drawing needle that you've dropped.
ALWAYS swab the vial top with alcohol before pinning it.
Try not to touch the vial top if you can avoid it.
Do NOT ever touch the drawing/injecting needle and then put it in the vial.
Do NOT double-dip between current and next vials (THEE premiere cause of vial contamination).
Et cetera.
Oh, and please don't toss it into your sock/underwear drawer...
DO keep it in a cool, dry place with minimal light exposure.
Dunces that failed to ply common-sense as above are why we don't get dispensed 10mL's in North America anymore (and now must pay TWICE as much for the bedeviled 1mL's).