We do the same, swap out the holiday art and put our regular decor on our bookshelves. We have switched to these tubs and they have been great. They are extremely sturdy and stack so nicely! Some of the cheaper tubs crack, but these seem pretty indestructible! homedepot.com/p/HDX-27-Gal-...
I usually have holiday storage containers I put my decor in. Right now I have to move things around in order to put up holiday items so when its time to store them again I just move things back to their spots
I do the same as the ladies above & return to my normal 9/12 month decor. This year I did find a table runner from Home Goods - would definitely recommend a pop into there for some refresher items! We also have the same tubs as Catherine Hazen & get them from Costco! The stacking feature with the lip on the lid is awesome!
Fortunately for us, we have a huge attic where we store Christmas decor. And I love the Target organizing containers. Valentine's Day decor is next for me, I can still keep the red decor from Christmas and add hearts!
We use large totes from Target, right now I have wintery stuff up (snow men, gnomes, etc.) until early February where I will switch to Valentine's day stuff.
I store mine in big bins labeled on the side. All my decor fits inside 3 of the bins. I don't replace it with much aside from the plants that always belonged there.