If you have possession of a Family Bible with important family documentation in it, you want to keep it as safely as you can. Southern Oregon Stories gave me some good tips on preserving a Family Bible.
Keep a Bible at room temperature 68 to 72 degrees. Maintain humidity as close to 50 percent as possible. Do not subject the Bible to extreme temperatures. So don't leave it in a car or store it in an attic or unfinished basement.
Store a Bible flat, but kept so that its form is not canted. Do not store it upright. Some people might want to leave it open on a Bible stand but that is not a good idea. Don't leave it open.
Preserve the Bible in an archival box. You can do a Google search on "archival boxes" to find what you need. They aren't overly expensive.
Store the Bible in the center of a closet (not the floor in case of flood and not on top in case of fire).
Keep the Bible family records on a separate note on acid free/lignen free paper inside the front cover with recognizable names.