As woof advises, many apples aren't suitable for storage... one site advises "...Tart and thick-skinned apples like Jonathans generally keep longer than sweet or thin-skinned ones like Delicious. Good keepers also have very firm flesh..."
Even small bruises on a single apple can cause spoilage... be sure to inspect them closely when wrapping. Additionally, the cooler you can store them the better. We have an older but serviceable fridge we use for winter storage. It's set at about 40 degrees (F) and we keep several varieties, all newspaper wrapped (not color sections though! Only black ink newsprint) and boxed...