I have found that the most important thing is a First Aid Kit. Hopefully you may never need it, but if you do! I took a small tool box and put all the necessary things in it that I needed in case of a small emergency. They sell prepared First Aid kits, you can google that search. If you travel with your horse, your vet will be able to help you with certain items he or she feels you may need.
I also keep hand sanitizer and Lysol Spray for my shoes. Should you have more than one horse and one gets a little cold, you will not want to go in and out of stalls with contaminated shoes. You can also fix a small tub to step into with a small mixture of Lysol and Bleach. This also works well for Dog Kennels. Do not spray your lysol in your barn rather outside at the door so as not to get it on your feed or water.
I keep sturdy paper towels in my barn along with a Dry Erase Board. I have in Bold Red the number of my vet and after hours emergency number. You will find that very handy. I also keep a calendar on the wall and write down everything I do and when the next round is due!