Another way of organizing your first aid kit is by having what you'll most likely need first on top. If you don't know what you'll most likely need first, there's the first problem. :-)

As another has said, the most important part of the first aid kit is your knowledge of how and when to use the stuff in the box. I've lost track of how many first aid courses I've taken, but it's remarkable how similar they've gotten over the decades. The people who do the training have gotten together and come up with fundamental principles and training, so the basics are being taught pretty much the same. This gives me confidence that I'm at least getting the standard first aid practices.

I'd really recommend a wilderness first aid course, even if you live in a city. I took a 2-day wilderness course that was the most thorough training I've had - much better than a 1-day overview, with lots more time to practice techniques. Practicing application of the bandaging and splinting is very important.

I'm in a CERT group, and our local fire department gives us annual training for free; check your local fire department for their offerings. They include urban search and rescue.

I'm not sure how widespread this opinion is, but the last guy I had a first aid course from did not hold Red Cross first aid training in high regard, and he thought their CPR techniques were behind current standards. shrug - I haven't had a Red Cross course in over 10 years, so I can't compare them to current training.

Good luck and have fun.