>>1271662You'd want basic, lightweight camping gear (tent, etc.) even if you're bunking down somewhere. Don't bother with things that won't last longer than a couple of months (such as gas cooking equipment).
Medical equipment such as bandages, tourniquet, antiseptic but also stuff for long-term treatment like stitches, antibiotics, etc.
Takedown bow for hunting, small carbine rifle for self-defence. Soft, light armour on extremities if zombies. Probably wouldn't bother with hard armour unless there's actually a serious risk of getting into firefights (like during an invasion or something).
Sewing equipment and whatever else for equipment repair.
Lots of water storage and filters etc.
Mostly you'd want prior experience and knowledge. Not much point hunting if you've never butchered a whole animal before, and I doubt many people could suture worth a damn. Also if the apocalypse is biological you'd want to know how to survive without meat (or if you could cook meat a certain way to not die).
Overall it's just long-term camping without a safety net. And maybe zombies.