It is better to store photos in paper than plastic if you want them to last centuries. While there are plastic storage boxes that specify they are acid-free, we don't yet know how prints will react with plastic over that long of a time. We do know that archival paper or cardboard storage can successfully preserve photos.  Plastic storage has advantages if you are more concerned about keeping them safe for short periods of time. It will be sturdier than cardboard or paper boxes, keeping your prints from getting bent or crushed. And if you get a sealed plastic box, your prints will be fully protected from water, rodents, and insects.