How I roll:
I use ziplock bags from the store. Quart sized bags fit most 6-7" scale figures. Gallon for the larger and snack-size for the smaller items (3.25", Hot Wheels, etc).
I use a metal paper punch and I stack up 8 bags at a time, or fold 4 in half, and punch a total of 6-8 holes down each side of the larger bags (3-4 on the snack). This makes the punch work better as it won't work at all on just one unfolded bag -- too thin and slick.
For accessories so small or thin they would fall through the holes, I put them in an un-punched snack bag and stick inside with the fig. Larger accessories I just put right with the fig.
Some plastics are ok without breathing for a year or two but in the long run it's surely bad for *all* of them if they can't. One thing that is very bad to seal off is any translucent DST minimates, they become tacky. Also, some figs/access will have rubbery material involved. If that can't breath it's usually the first thing to go bad -- it can become brittle, or, oily, from my experience.
Next is what type of tubs you store them in. I have both open-air tubs that act as drawers (
these ones here, which stack up nice in the closet for a giant storage solution) and I also have some flat horizontal stacking tubs with loosely attaching lids. I would never put them in any snap-tight, air-tight type of tub+lid.
And finally is *how* you put them in the tubs. If you lay them all in there and pile them on top of each other, most likely they will press down on each other and end up blocking most/all of the airway holes you punched, defeating the purpose. Instead, I try and stand them upright, loosely packed together, and if the tub is tall enough, stand another layer upright on top of that layer as it fills up.
Sometimes I take an entire wave of figures and put them, bagged, inside another larger (1-2 gallon) hole-punched ziplock. When they are in there snug it can help to make sure there's an air path for all.
I just opened up a 2005 NECA Dr. Finklestein the other day (wow, old as this thread!). Correct me if I'm wrong but the NECA blister packaging doesn't seem to breath in any way. It's why we get that NECA smell. His arm joints disintegrated on first attempted movement. I'm blaming being unable to breathe for so long since the bubble didn't show UV damage. They gotta breathe!