There is a world of difference between something like what is known pejoratively as a booboo kit and something like a military grade squad level trauma kit, or even a booboo kit and an IFAK.
There are plenty of reasons for this, the most glaringly obvious of course being that the average person in a home or workplace is far more likely to suffer from a booboo rather than, say, a gunshot wound to the chest and attendant pneumothorax. Another one is that many things used by soldiers, paramedics and corpsmen require special training to even know when to use, let alone know how to use, and are used under very, very different circumstances.
But, that doesn't mean that some of them can't be helpful to have around for the average person. The Everyman's First Response Kit is most certainly not intended to be a booboo kit. It's something that would live in the hall closet or the trunk of your car and be used for situations that merit it. None of the things outlined below require any special license or permit to have, and all are available "over the counter" in the United States, and more than likely elsewhere, though I don't know that for sure.
This kit will equip you materials-wise to handle most common trauma, at least well enough to suffice until professional help arrives. The emphasis is not on treatment, but immediate treatment of serious trauma. You are not going to be stitching up a deep gash or performing deep disinfection, you are going to be getting the big chunks of gravel out and covering it up long enough to get to a hospital. You are not going to be throwing down antibiotic dressings on deep burns, you are going to be slathering it with wet dressings to ease the pain and stop the continuing damage.
Dressings and Bandages
It's important to note the difference between dressings and bandages. Dressings cover a wound; bandages hold dressings in place.
Dressings are anything from clean rags packed into a wound to purpose made gauze squares.
Bandages come in many forms, and can be improvised from a scarf, or purpose made, such as what is known colloquially as "vet wrap". 4-inch vet wrap is the best stuff. Vet wrap is stretchy, relatively tough, and sticks to itself but nothing else. Imagine a disposable ACE bandage that sticks to itself rather than requiring those dorky stamped aluminum clips.
I highly, highly recommend what are known as "Israeli bandages". They go by a few different trade names, but all operate on the same concept; a dressing, bandage, and fastener integrated into a single unit, easily applied on almost any body part with one hand if necessary. Israeli bandages are the best, though the Olaes Modular bandages are excellent as well.
QuikClot and its workalikes have received a lot of press over the years. They are extremely effective and their latest incarnations are extremely safe. Absolutely do not use the granulated powder form of any of these substances; Use the sponges or integrated gauze. The granulated forms pose a hazard to eyes and mucous membranes, and require extensive cleaning of the wound beyond what is necessitated by the wound itself when the patient reaches primary care (probably the emergency room or hospital). Note that there is a shelf life for these type products, usually 3-5 years.
Splints, collars, and tourniquets
These are slightly specialized pieces of equipment. Well, other than splints. I highly recommend the formable and bendable "SAM splint". They're a sheet of aluminum sandwiched between closed cell foam, and can be bent, molded, and shaped to fit any contour on the human body. They can actually be used as a cervical collar in a pinch, can be trimmed with common scissors if necessary, and are strong enough to be used as a shovel if bent right. Also, they're reusable.
Collars (cervical collars) absolutely should not be used by anybody without official and professional training. Improper use of a collar can cause severe damage to someone with a neck injury above and beyond the damage caused by improper handling of a suspected spinal injury.
Tourniquets are a tricky thing. They do require quite a bit more training than something like an izzy bandage or a SAM splint, and traditionally are meant to be a thing of utterly last resort. However, as is the case with most wars, the current conflicts in Iraq and Afghanistan have shaken up much of the established medical establishment in regards to traumatic injury. I will not attempt to instruct readers on the appropriate use of a tourniquet, but will say that if applied properly they are much more effective, and much less dangerous, than they are traditionally viewed to be.
Oils, salves, unguents, etcetera
Burn gel is probably the only thing you need to have in a kit like this. There are several brands on the market. Water-Jel is the brand I recommend, and it can be used in conjunction with a dressing on serious burns, or alone on minor burns.
Other than Water-Jel, a large bottle of water or saline wash to remove large foreign debris from a wound is not a bad choice either. Note that saline does expire, and water doesn't, if kept in an appropriate container.
Safety equipment and tools
Purple nitrile gloves, several pairs that you know fit, and a decent pair of EMS shears are essential.
A small, clean, sharp pocketknife will be useful to turn your waterbottle into a squeezebottle with a jet, or to open packages.
3 ct. Israeli Bandage (6-inch size)
5 ct. 4x4 Sterile Gauze pads
2 rolls 4-inch "vet wrap" or "self-cling wrap"
1 roll 2-inch medical tape
1 ct. Quik-Clot 50g Mesh Bag
1 ct. SAM Splint
1 ct. package of Water-Jel packets
1 ct. 1 liter saline wash or 1 liter water in squeezable bottle
3 pair purple nitrile gloves
1 ct. EMS shears, large size
1 ct. Leatherman Micra (or similar - the Micra is great here due to its small size and decent scissors)
Everything here can be purchased online (chinook or amazon to start), and, aside from the Micra or similar, for less than a decent restaurant meal.
Now comes the really hard part: Getting training. Just having this stuff doesn't make you helpful, it just means you blew $50 on some cool looking kit.
Outside of the military, where you'll learn to use all of this and far more (nasopharyngeal airway tube, intravenous drips, Asherman chest seals, morphine, atropine, tourniquets, just to name a few), your options are EMT-B training (available at many community colleges for a few hundred bucks, and the courses typically include EMT-B initial certification) or organizations such as the Red Cross.
The Red Cross offers instruction in everything from CPR to First Aid to First Response, and in some areas, EMT-B courses minus the certification. Most of the courses are free or very low cost.
You may not be taught to use these exact items, but a good first responder course will give you the knowledge, theory, and hands-on time that you need to be able to apply everything in the kit to good effect.
There are certainly many, many books out there that can give you a rough idea, and most of the items will have instructions for use printed right on them, but there is absolutely no substitute for hands-on practice and instruction from a qualified teacher.
The suggested kit above is good materials-wise for everything from multiple gunshot wounds to road rash. You'll notice there are no band-aids, so take your booboos elsewhere!
Auduster says re Everyman's First Response Kit: Hmmm... I looked at this with the immediate thought of "how does this compare with my solo mountaineering kit".. Answer - almost no crossover at all, beyond the splints, bandages and dressings... There's a heavy emphasis here on not-bleeding-to-death... Might be worth mentioning this.
Auduster makes a good point here, in that I perhaps did not adequately address the intended uses to begin with. This kit is not meant to be something you would use in the wilderness or far away from professional help time-wise. This kit is intended only as a first response to grievous injury, such as a serious car accident, burn, stab, gunshot, or other major trauma. It's meant, in the worst of cases, to keep someone alive long enough for the pros to show up, and in the best of cases, to get someone stable enough to get to a hospital.
Something like a wilderness medicine kit is going to be much more extensive, and would include quite a few more things, like butterfly strips or other field sutures, multi-sized bandages, slings, moleskin, glucose syrup, antihistamines, even temporary casts!
Most of the items in this kit are dual-purpose, though it may not be immediately obvious. An extra Israeli bandage becomes a sling; 2" tape secures a limb into the splint or immobilizes broken fingers, water is drinkable, but it is most certainly not an extensive suite of treatments!
The bottom line is, get some rudimentary training for whatever environment you're expecting to deal with, and supplement or build up a kit accordingly!