For most climbing/hiking/mountaineering/backpacking trips, my first aid kit:
Acetaminophen & Ibuprofen - a couple days doses worth of 500mg tablets, in a small ziplock labeled with dosage/expiry
Other medicines - for me, it’s allergy/asthma stuff, depending on the season
For everything else - "bandaids", covering blisters, steri-strip style stitches, making splints, repairing gear1
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After ~20 years of trips, that's what I've repeatedly, actually, used for dealing with a range of backcountry injuries and illnesses. (My own, and others in my party, and occasionally people we pass on the trail who need help.)
And besides "actually get used" (clearly the most important), it fits all the other critera: inexpensive2, easy to refill, lightweight.
I put the pills in a small plastic container3, wrap the duct tape around the outside. For longer trips, I bring a safety pin, needle, and small amount of thread for lancing blisters and gear repairs. Sometimes two or three bandaids and a roll of gauze, and some real steri-strips. Since it’s a good place to keep other Ten Essentials-ish stuff, I stick a few water treatment pills and a lighter or matches in there too.
Certainly the point is not that I think this is exactly what you should do, but that what you repeatedly use is probably less than you think, and you could make your life lighter/more inexpensive if you do a bit of taking stock. For me, it could really just be pills and duct tape, wrap the duct tape around something else and toss the bag of pills in the pack. The bigger kit I use feels very decadently prepared.
1: Some ways I use duct tape: 1. Instead of bandaids: tear off a rectangle and a small square. Put the square on the rectangle, sticky sides together, so it looks like a bandaid. Use that to cover wounds and blisters. It's really great for blisters, I find it to work way better than moleskine or any blister-specific products. 2. Steri-strip/stiches replacement: tear/cut into 2-3mm x 10-25mm rectangles and place 3-5mm apart to close wounds. 3. With sticks + material (a bandanna or part of your clothes/pack) to make splints for injuries. 4. Patching holes in clothes or gear.
2: Key part of being inexpensive is not buying the individually packaged pills or any of the other stuff that comes with pre-made first aid kits. Just take the pills you usually use, and put them in a small ziplock. Label it in a way you can tell them apart, with dosage and expiration - sharpie on the bag, or a slip of paper inside it.
3: Not sure where the plastic box I've been using came from. Adam uses a discarded Nuun (or Airborne?) tablets container for his, and I might switch to that and pare down even more. It's nice to have something waterproof-ish.