Purchase a basic $10 first aid kit or two to have on set. This will cover you for the basics including bandages, antiseptics, and a chemical cold pack.
Make sure to add the following 3 items however:
A tube of triple-antibiotic ointment (brand name Neosporin – but who buys brand name?) Apply to all nicks and cuts before bandaging. Also great for chapped lips.
A bottle of acetaminophen (Tylenol). Don’t offer anything else as acetaminophen has the fewest drug interactions and is the ONLY pain killer appropriate for kids.
A handful of Lipton teabags. Place wet teabags on a burn immediately. The tannic acid helps draw the heat out of burned skin and greatly reduces the severity of the burn. Keep applying cold water over the teabag until the pain lessens.