I received my first aid training in the military and kept it up in civilian life. You're right, knowledge is the most important thing, but a kit makes things much simpler.
Long ago I got into the habit of carrying a first aid kit whilst shooting. I tend to stalk alone or with a partner, rarely with a professional stalker. I use a small webbing ammunition pouch attached to my belt and carry the usual band aids, some small bandages,alcohol swabs, safety pins and butterfly sutures. Also some aspirin or paracetomol and I wrap the whole lot in a plastic survival bag, in case I can't walk out and need protection from the cold and wet on the hill.

The most important thing I carry however is a large shell dressing, for major wounds. it can be tied in place and if need be packed with clothing or anything else handy. I also usually carry a length of paracord and a good knife. ( I have a swiss army hunter in my pocket and a Cold Steel SRK on my belt ). the whole shebang weighs about a pound or so and is unobtrusive on the belt.

In africa, I carried this minus the survival bag. As previously stated, the Outfitters First Aid kit was always left with the vehicle.