Light is damaging to old books, so they are best stored in a dark place. Book boxes are a good option, but they can be expensive, so I store mine in Ikea bookshelves with opaque doors.
Never put antique books in plastic or seal them in a closed container. They need to be allowed to breathe and kept away from moisture. If using book boxes or closed storage, put packets of silica gel (the kind that come in shoe boxes) with the books to absorb extra moisture. After having particularly humid weather, remove them from the book storage, allow them to dry, then replace them.
Modern books are printed on acid-free paper that withstands aging, but antiques almost never are. Protect books by wrapping them in acid-free paper. This is easily available in big tablets that are easy to wrap around books, but make sure to leave an opening at the top—books don’t like to be sealed. Write the book’s title, author, and publication date in pencil. Pencil is far better than pen for archival purposes and will not deteriorate the way ink does. In college, I spent some time developing glass-plate negatives from the turn of the century, and all archival writing had to be done in pencil.
To prevent spine/cover damage, the best way to store antiques is to stack them on their sides. However, books seldom fit in bookcases this way. If storing books standing up (the normal way), you must deal with that gap between the bottom of the pages and the bottom of the spine. Fill this gap with acid-free cardboard or folded paper of appropriate thickness. If you are wrapping your books in paper, then the wrappings will easily keep this support paper securely in place.