Preserving Books: What cover should I use for this? How do I prevent warping?

I have some vintage books that have a picture on the cover. Some old books (19th century-early 20th) had a cloth cover and then a color picture was pasted on it. How can I preserve these types of books?

For my regular older dustwrapped books, I use mylar Brodart covers. For my vintage paperbacks, I use the plastic covers that are customized to the size of book. I am not sure what you would use for these older books…except plain mylar? Yes? No? Ideas?

Also, I keep these books on my bookshelf and noticed that they are getting warped. They are kept at room temperature but the books are warping. The covers are bending upward a bit…away from the pages. Any ideas on how to keep them from doing this?

Thank you very much!