We've always had a problem with the order of things in Maslow's hierarchy of needs. From our perspective, stopping the bleeding is always job one, well before food, water, shelter and even sex. Let's follow the critical path: trauma is the leading cause of death for people up to age 45, and uncontrolled bleeding is the leading cause of death from trauma. Ipso facto, if you're going to be prepared for one thing, it should be the training and gear to control bleeding.
Training is available from many sources, just be sure you're not getting the ubiquitous "first aid" class that doesn't teach tourniquets, chest seals and airway management – the big three when it comes to casualty care. NOLS has a series of wilderness medicine courses from a 16 hour Wilderness First Aid to the 200 hour Wilderness EMT. Private companies like Dark Angel Medical offer courses all over the country. If it's at all related to your job, your state probably has a list of trauma courses for credit, as likely will the university or community college near you. If you're really tight on cash, find some reliable video training online. The point is, there's not excuse not to get some training.
So what's in a minimalist trauma kit?
Tourniquet, clotting agent and bandage for bleeding; chest seals for open chest wounds; and maybe a nasal airway for breathing. So, bleeding first, and that starts with a quality tourniquet. Do not buy cheap tourniquets: if it costs less than $10 it probably will fail. The standard in tourniquets is the NAR CAT, the official tourniquet of the United States Army. It's a windlass style tourniquet, just slip it over the limb, tighten it up and clip it off. All of this can be done with one hand. A less expensive but still high quality alternative is the Recon Medical tourniquet, which comes in at about half the price. Get one, practice, and keep it handy. For clotting agent, QuikClot gauze is the standard, or Zeolite sponges. Place over wound and wrap with more gauze or better, an Israeli battle dressing (we like the mini version from H&H Medical), quick and easy to apply and exerts extra pressure on the wound.
For chest seals you can theoretically use any non-permeable membrane like a plastic bag or the like, but since you believe in preparing before the need arises you'll get a twin-pack of Hyfin chest seals, which have a nice self-adhesive design for quick application in a high stress environment. HALO makes an alternative at about the same price point. The reason for two is one each for entry and exit wound, although in a pinch – say, multiple casualties – you could use the seal for one and the wrapper for the other, if you're carrying surgical tape or some other means to affix the material to a sweaty, bleeding hairy surface.
Finally, you may want a nasal airway. These are trickier to apply, and much less likely to be needed than the tourniquet, QuikClot, Israeli bandage and chest seals, but hey – it's small so why not? So what have we omitted here: sterilization is not necessarily your first concern when someone is bleeding out, but Povidone-Iodine swab sticks might come in handy, plus nitrile gloves, mini shears, extra gauze, surgical tape, wound closure strips (2×9" Phokus Frog Tape and 0.25×3" 3M Steri-Strips), triangle bandages and eye shield are some of the more common things in trauma kits. Still paranoid you're forgetting something? You are! Hypothermia is part of the trauma triad of death for a reason, and a mylar blanket takes up very little room. For the minimalist however, the combination of the items we've covered here will make for a compact kit that covers the most likely scenarios. Put it all in a heavy duty Ziploc bag (we use a Granite Gear 1 liter ZippDitty) and you're good to go.