As a Corpsman, my job in the military was to put band-aids on Marines and hold them when they felt sad. I received a decent amount of medical training during that time and also had a small bit of hands-on experience (mostly treating wounded Iraqi children and inept terrorists). I was not a SARC and did not go through the 18D pipeline. Before joining the Navy, I worked in an emergency room as a physician's scribe. These experiences have shaped my outlook on emergency medicine and the equipment I carry for first aid purposes.
Recently, I have noticed more people talking about what first aid kit or trauma kit they carry or own, which is a good thing. However, having a band-aid is only part of the equation when it comes to treating a cut. Unlike being in a gunfight, for which not bringing a gun is a cardinal sin, first aid can often be improvised with available materials while help is summoned. Some of the most serious injuries I have ever dealt with were treated with inadequate supplies. Realize that as a first responder, the best thing you can do is to get your patient to a higher level of care as soon as possible.
Vitriolic Tangent About Training
While it is popular in the gun world to "get training" (and I definitely think you should attend the ones I teach!), it does not seem as popular to get training in other areas - driving, first aid, etc. Think about it - how much time do you spend driving each day versus how much time you spend in a gunfight each day? How many people are killed by drunk drivers each year versus armed criminals or terrorists? Why would you bias all of your training towards firearms instead of spreading out your expendable income to include a high performance driving course? Similarly, why go to more than one firearm training course before you know basic first aid? Excuses for not attending Bondurant include the fact that it's really expensive, but basic CPR and first aid courses are generally available through the Red Cross for affordable prices.
If you haven't kept current with first aid in a while, a refresher might not be a bad idea. For example, CPR, which was once called "rescue breathing," has now changed into "continuous chest compressions." A few years - or maybe a decade - ago, there was a pretty wide separation between military and civilian medical training. Lessons learned in Iraq and Afghanistan seem to have trickled down to those in fire departments and EMS, although I can't say that everything is now being taught the same way on both sides. However, whether you go through a Red Cross class or a Combat Aidsman course, I think you'll be well ahead of someone who hasn't bothered to get any first aid training. For that matter, a 12-year-old Boy Scout with his neckerchief and a stick will be light years ahead of someone with a fancy trauma kit and no idea how to use it.
Okay, back to the topic at hand.
Stuff I Generally Keep In My Car
I have a lot of medbags thanks to my time in the military - mostly Unit Ones and a big London Bridge bag. However, one of the most useful first aid kits I own was purchased after I got out: an Adventure Medical Kits Guide 1. It was discounted heavily on Steep and Cheap, so I didn't pay $270 for it. However, I've gotten plenty of use out of it and try to keep it replenished. I'll cover individual items later, but a good kit like this will cover most of your needs. Even a $20 kit at Walmart or Target has the basics.
Although the Guide 1 has some items for treating trauma injuries, I also carry a kit of my own assembly. This generally consists of tourniquets, pressure dressings, chest seals, 14 gauge IV catheters, SAM splints, ACE bandages, abdominal bandages, and Water-Jel. Putting together something like this from scratch with the basics (mostly just tourniquets/pressure dressings) shouldn't be too expensive. I like using brightly colored bags or keeping the kit in a larger, easily recognizable bag so that I can tell someone to run to my car and grab "the big red bag" or something like that, rather than tell them to grab the khaki pouch in the trunk full of khaki, coyote, tan, and brown items.
I use the CAT tourniquet because I have seen it work well, but I would not be too particular about the type as long as I could apply it to myself or others without too much difficulty. Some people say that the CAT windlass breaks easily, but I haven't seen that - it's something to consider, but as long as you know how to apply it properly, you will be fine. I was issued Cinch-Tight pressure dressings and have not seen a need to look for anything else.
Chest seals - I was taught to improvise them (using an ID card taped at three corners over the wound, allowing air to escape but sealing fairly well against the entrance of air) as well as use the Ascherman, although the HALO is supposedly better; I have not had occasion to use the HALO, but much like the CAT, the Ascherman works well if you know its failure points.
The IV catheter is for relieving tension pneumothorax. I was trained how to use it, although it's up to you as to whether or not you carry one. If you take my advice and seek out training, this won't be an issue.
The SAM splints and ACE bandages are for joint immobilization; this can be improvised if the patient needs to stay in place, but if you need to move to a pickup point, having good supplies for joint immobilization might be invaluable.
Finally, the Water-Jel is for treatment of burns.
I also like having an axe or large hammer in my car, and a knife in my pocket. These items can help free someone if they are trapped. Oh, and I bring nitrile gloves, too. I also have a prepaid cell phone with up to date service with a different provider than my normal smartphone just in case said normal smartphone is dead or doesn't get service when I need help.
Stuff I Carry With Me In A Pack
It's okay to put a big bag of stuff in the trunk of my car, but do I carry all that stuff with me on a day hike? No. I'll generally bring a small kit with band-aids of various sizes, Neosporin, alcohol pads, ammonia poppers (to wake up dead people), gloves, ACE bandages, Kerlex, some 4x4 gauze pads, NSAIDs (generic Naproxen most of the time) as well as an Epi-Pen (I don't have allergies, but other people do). You'll notice that I don't bring the majority of trauma kit items, and that's because they're far less likely to be needed. You don't want to be the guy standing there saying "Sorry about the scraped knee, but I can only help people who have been shot in the chest or leg."
Understand the human body, the mechanisms of injury which it is likely to encounter, how the body responds to these injuries, and how you can help the body in this fight until help arrives. Have appropriate tools if possible, but focus on understanding first.