This is what I always have on set:
Protective gloves, depending on your department this will vary.
A Leatherman, because you always need a multitool. A small emergency pack with respiratory protection so I can give mouth to mouth air without having to touch the patient.
My medicine box.
Keys.
I call the picture filmmakers flatlay.
we have a big first aid kit on set. This is a special piece:
A face shield for CPR 
You can learn first aid basics in a 2 day course and usually your employer pays for it. As every company with a certain number of workforce has to have a dedicated first aid person at work at all times.
You can learn the basics from any nurse or healthcare worker as they have to know too. Unfortunately this course has to be a hands on thing because you are practicing techniques on how to safe a persons life.
It is also mandatory to have a course if you want to get your driving license.
I understand, I mean...
Taking a first aid course has a lot of job opportunities? sounds interesting!