Anything with holes in to allow air to get around. Or, in extremis, (and I really mean extreme), supermarket carrier bags. Up to now I have used mainly collapsible plastic storage boxes, the ones with holes in, and put just a couple of layers of apples in the bottom of each. DH has now converted a wine rack into an apple store, with slatted wooden trays to fit the shelves.
I don't wrap each apple individually as it make inspection difficult, and regular inspection is key. So anything where you can lay the apples out in a single layer.
You need somewhere cool and not too dry. I put them in the cellar, my parents used the porch on the N side of the house, DH's parents used cupboards in the eaves. Nowadays people recommend the fridge - you'd obviously have to buy another two or three fridges 
Anything which has fallen from the tree can't be stored. It may look perfectly good but it will rot.
I don't think pears can be stored either - they go mushy in about two weeks flat. You need to use them immediately or cook them and freeze them.
The length of time that apples can be stored depends on the variety - some last only 2-3 weeks, some are good until March. Very roughly, the later a variety ripens, the longer it can be stored. So the ones falling now won't last long, but the ones that are still firmly on the tree when you pick them late October/early November to avoid the frosts will carry on ripening in storage and be good to Christmas and beyond. You can tell when an apple is ripe to pick because it will part easily from the tree when you lift it.