You should always carry an equine first-aid kit when traveling to shows and trail rides. It's aggravating, however, to search through rolls of tape and bandage material just to find your thermometer in the bottom of a box or bag.
The best container I've found to store my first-air supplies is a large fishing-tackle box with drawers. A two- or three-drawer tackle box provides lots of room in a handy carrying case, and numerous compartments to help keep items separate and easy to locate. You can store smaller supplies in the individual sections of the drawers, and place larger items in the bottom of the tackle box. I've used this first-aid kit for several years and have found it both sturdy and convenient.