I carry a very minimal kit as well, mostly focused on things that are annoying but common rather than serious injuries. Band-aids, antiseptic wipes, blister pads, painkillers, and antihistamines usually cover most situations for me.

For the container, I’ve had good luck using a small zippered pouch from an old amenity kit or toiletries bag — gives a bit more structure than a ziplock but still stays lightweight and easy to pack. Anything beyond that, I usually rely on local pharmacies once I arrive.