First aid training is first.

Of course the usual bandaids, gauze, tylenol, etc. A luxury item in my first aid kit is Soothe-A-Sting Swabs . I also usually carry ointment for cracked heel, an antibiotic ointment (Neosporin or similar) and tweezers with magnifying glass. Sometimes I will have some peroxide or alcohol wipes disinfecting.

Not necessarily part of a first aid kit but related: hand lotion to prevent chapping, lip balm/chapstick, and of course sanitizing gel to keep hands clean for eating.