Store it at 2 - 8 degrees C (so in the fridge).
When I use it, I place it in a clamp stand so it cant fall over in the fumehood. I use needles to take it up and add it to my flask dropwise.
Any needles, syringes, glassware etc, is left in NaOH solution overnight.
I wouldnt use vacuum distillation only because its nasty carcinogenic stuff. After work up, I will use a rotary evaporator but I would never distill MOM-Cl before use.