Having spent 27 years in elementary schools, I know that what one teacher considers essential, another might consider optional -- or supply herself -- and that it's possible to successfully "go cheap" on some items. But, since this is "3 Keys Thursday," I'm going to focus on three basic, important items that are worth spending a little more on, since they're key tools for staying organized all year long.
A home for papers that need to be referenced. For many kids, this is a three-ring binder. It can also be an accordion folder (or one for each subject, for older kids), a skinny binder with a clamp closure (or one for each subject, for older kids), or a collection of folders color coded by subject. Whatever it is, it needs to be durable and expandable so that it can house everything from a single sheet of paper to several fat packets that cover entire units of study. These should live in the desk at school unless they're explicitly coming home so your child can study for a test.
A home for papers that need to be dealt with (homework, need signatures). For younger children, these are the papers that go in the "take home" pocket of a two-pocket folder. If for older students have demonstrated success with this system in years past, there's no need to come up with something new. If pocket folders don't work, try file folders, top-loading "backpack" folders, or an accordion file divided either by subject or by whether the paper stays home or goes back to school. Whatever you child chooses, it should be big enough to hold a stack of papers, but not so big that a single sheet of paper gets swallowed up, and it should be durable, as it will spend a lot of time traveling back and forth between home and school in your child's backpack. Many teachers have a required system for this, so before your child gets too excited, make sure his or her system will be acceptable to the teacher.
Older kids who travel between classrooms often like flat pencil holders designed to fit inside three-ring binders. They're typically carrying fewer supplies than younger kids and portability is more important than capacity.
Regardless of your child's age, make sure to take attributes like size, visibility (clear containers help I know I put it somewhere and I need to see it kids remember what's where), ease of use and durability. Again, this container will get a workout.
Finally, as you're making your purchases, consider how the three key container attributes (form, function and style) of the chosen supply interact with your child's personal and organizational styles. The closer the fit (and the more excited your child is about using the item), the more likely it will be used beyond the first month of school.
One last suggestion: If your child's school doesn't supply some sort of planner or assignment notebook, that should be at the top of your list as well. Your child may choose to integrate it into his or her home for papers that need to be dealt with, or carry it separately, depending up the tool he or she decides on for the papers that travel between home and school. When schools provide online assignments, many kids need a hard copy back up as well; actually transferring the assignment from the computer screen onto the page serves as a memory tool for some kids.
It's possible to spend endless hours (and nearly endless dollars) in the school supply section. As always, start with successes (what worked last year? what didn't?) and build from there, to make sure this school year starts and ends with STYLE.