As you know, I like simple solutions. A very simple idea for storing your kids' artwork and school papers is to grab enough large transparent bags and Command hooks for each child. (Ziplock makes Big Bags which are shown in the photo.) Choose a closet and hang your command hooks and bags making sure to label each bag with your the children's names.
During the school year, make it a habit to put kid-creations that are worthy of keeping into the bags each night after they dump their book bags. When the school year ends, sit down with each child and go through their bag to determine which pieces of art are favorites and which can be discarded. Now take the bag, label it with the grade the child just completed and place it in a plastic tote where you will save a bag for each grade the child has completed. I like to suggest the Wheeled Underbed Box by Rubbermaid because they are large enough for bigger pieces of art and can easily be stored under each child's bed.
Having a simple plan to corral these papers at the start of the school year is sure to reduce stress and clutter.