We keep apples in cardboard boxes on the floor of our front door coat closet, that overhangs into our attached garage--keeps them at about fridge temp during the freezing months, for now we keep them in the cardboard boxes sitting on the basement floor which is not quite cold enough but most are still on the trees and we won't pick them till we have to. I would never keep apples in plastic, they off-gas and need to be kept away from other produce unless you want it to rot, especially potatoes. They can be stored near carrots though.
There's another thread around here about keeping potatoes, we haven't grown a large amount of keeping potatoes since our old house which had a big wooden potato bin in the basement cold room (insulated from the rest of the basement) so we just keep them in buckets of sand--no lids. But we only buy about 3 months worth of potatoes at a time from the farmers market a couple of times throughout the winter, so they aren't keeping for very long.
We've just put up 60 lbs of carrots in 5 gallon buckets layered with sand, lids sitting loosely on top--we keep them in our cool basement guest room next to our shelves of home canned food--has always worked well in the past for us. This also works really well for beets and parsnips, but this year we had a pocket gopher eat nearly all of our parsnips (from the bottom up!) and our beets didn't do very well so all that we harvested went straight into borscht for canning.