For organizing toothbrushes, and each child's personal care items, our kids each have their own bucket. They put their shampoo, hair brushes, soap, etc. in it. Many of these items are shared, but as the kids get older they find they need their own things more and more.
Buckets are nice because they are easily washed, easy to carry, don't take up too much room and can be stored in a closet, on a dresser, or on a shelf, depending on the situation.
These are my tips for running a large household - for tips on handling life in general, check out Tips for Success.