I sort of do both.
Around 1st Dec, the advent calendar comes out (we have a reusable one) and my box of Christmas books and dvds. These have been gathered over years, and are a mix of short kiddie books and larger bedtime stories, cartoons and movies, Some are kid friendly while a few are more adult (eg Die Hard as well as Home Alone). When dd was younger, I also brought out a shoe box filled with strips of different coloured paper and tape, which she could make into paper chains for when we decorated. I usually also bring home from the storage unit a handful of Christmas mugs and a fleece blanket with Santa flying on it, and DD's Christmas duvet set. All things we've had for years (and a few pre-dated DD).
On 24th, in the evening after dinner, we light the Christmas candle and then the Christmas Eve box comes out. This holds new PJs for all 3 of us (DH, DD and I), which sometimes are festive but often not. Some years, there might be slippers or fluffy socks as well. It also holds a seasonal ale for DH and nice hot chocolate for dd and I (the lump of chocolate on a wooden spoon type, and mine sometimes has a little container of alcohol stuck into it).
But it also contains a number of items that are reused every year - DD's stocking, her plastic Santa plate and glass (from when she was a toddler) for Santa's snack, and the family copy of "Twas the night before Christmas" which is our traditional bedtime story on Christmas Eve.
1st Dec items just come home in boxes/bags from storage, there is no chest involved.
24th Dec items go into a cardboard box that was a wrapping for a present years ago - we use it to hold the books/dvds most of the year but it changes on 24th to being the hamper, and then back to being storage again.