I started by looking over gear lists on this & other websites. After that, I asked myself what would be good things to have on hand in my climate if things like electricity & gas went away for a few days. We live in the chilly & wet pacific NW, so I started saving old clothes & raingear to keep in the garage and car trunk. We identified our likely neighborhood dangers as fire, flood, and burglary, so we now have a fire/flood safe on our shopping list. I also signed up for an online service that sends emails & text messages whenever the rivers start to rise.

What you should keep on hand really does depend on where you live... for example, I grew up in a rural town on the Alaskan coast, and about every year we had to evacuate to higher ground because of tsunami warnings. In that case, it made sense to be able to get the car packed for an extended camping trip in under 15 minutes. Preparing ourselves like that makes little sense now that we live in the city. We still have camping equipment, but now it's for leisure.

As far as daily carry gear is concerned, I basically expect it to get me to my house, car, or work, and from there I'll be better set up to deal with things. I don't lug around much with me except a canteen, umbrella, first aid kit, book to read, pepper spray, and wallet & keys & such. I don't bother with a compass, firestarter, etc. unless I'm going on a hike.

Getting training helps bring things into focus. I've taken first aid + AED for professionals, wilderness first aid, and an edible wild plant class. Soon I'd like to take a CERT class, and I'm looking for another martial arts dojo to join now that my current one has closed. Getting trained is empowering and helps build community.
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"Let us climb a mountain, hanging on by low scragged limbs." - Roger Zelanzany