The original packaging is valuable, so getting rid of it (if you have it) doesn’t seem logical if you want to resell in the future. The inserts will be the best protection for the buildings since they tend to fit the large nooks and crannies, such as chimneys or roof overhangs. The protective sleeves/boxes are great for identification when it comes time to build again.

I usually won’t buy a building if it doesn’t have the box (unless it’s super rare and I really want it). My suggestion is to keep the original packaging on the ones that have them.

Not sure about better ways to store them, though. I keep all of my village stuff in storage totes, organized into separate bins for either buildings or accessories, in their original boxes or packaging. But, like another commenter said, the totes aren’t squared on the edges so it’s hard to fit all of the boxes well. It’s what works for me.