I don't driftboat, but raft whitewater. Understanding you're asking about what you need for drifting:
Lots of rafters I know carry something like the NRS Pro Paddler first aid kit as a starting point for day trips, overnights and for each boat to have on multi-day trips. It's got lots of things you'd want and can be supplemented with extra tape, trauma bandage(s), extra meds, CPR mask, etc. when desired. Folks going on more significant trips will want a much more comprehensive kit with the group.
For training I personally think everyone should have at least Basic First Aid & CPR as a start, then move up to Advanced.
They say most boating accidents happen within 10 feet of shore, so I'd expect your risk rises when you pull over to shore, tie up, and go wading. And you never know when you'll be the one rescuing yahoos that didn't bring anything.
Others may chime in with more comprehensive recommendations.
Most of us on this forum are white water enthusiasts. Thus, we may have different need for first aid in that respect. White Water kayaking can involve different first aid needs from day trip white water rafting (class III and above) and more comprehensive for expedition white water rafting or kayaking. I would encourage everybody on the river to have a basic kit and supplement that for what you see as possible injuries and issues. I would also encourage you to carry a pin kit if you are running any white water. Having a basic knowledge of first aid and rescue is paramount. That means taking classes and practice. Certifications in Basic First Aid, Advanced First Aid, Wilderness First Responder and Swiftwater Technician I and II are great.
You really don't need all that much to be worth while in the wilderness. A basic first aid kit + some basic training (CPR and First Aid) is all you need. Learn some basic skills and hope that you never have to do anything invasive in the field. I'm a doctor and my first aid kit fits in a 1 gallon zip-lock bag that I carry in my dry bag. Even the wilderness kit (like going to Africa) can fit in something this size, and that's with a full kit worth of invasive gear too.
The "KISS" deal is a good motto when you're in the wilderness, whether you're a basic first responder or a neurosurgeon.
I second GAtoCSU. Training trumps stuff. I think a wilderness first aid or wilderness first responder that has a good emphasis on austere environments is key.
My kit is made up of the things that I think I can't improvise, that can care for minor issues, and that will allow me to either prevent an evacuation or stabilize until an evacuation. My "major" kit lives in a regular ammo can, and contains a small dry bag with my "minor" kit for hikes.
Really bare bones: tape, safety pins, a knife, ibuprofen.
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