The apartment building I live in is for older people on limited budgets and for handicapped people. They provide very nice living conditions at a percentage of income. They also supply various events for tenants, such as an emergency plan meeting a while ago, along with a basic emergency kit. They stressed that the kit should be somewhere like the closet next to the front door. They said "it should be in a place where you can grab it as you escape."
I suspect that it's not practical to keep all of it there all the time. I suspect that one emergency kit with an extra bag or backpack would be good if you (for instance) keep all your medications in a bag so that you can grab the bag and stuff it into the bigger bag as you flee. And have several more convenient points where other parts of the finished kit are stored so it can be actually assembled very quickly.
The kit they supplied is very nice, but is only the beginning of what I would really need. I've been meaning to update it, but haven't gotten around to it. So, I though about looking up the kinds of things that I should keep in that kit, and I found a website with a great list of stuff for a kit, plus lots of other points that I hadn't thought of.
They mention a flashlight and extra batteries, but there are hand cranked flashlights available, and they might be helpful longer than one that uses batteries. And of course, you'll want a sturdy bag or other container that's easy to carry.
Actually, I think that all this would be too much for me to carry, but even just some of the most basic items would be a big improvement over nothing.
Please do explore the whole site. There are lots of links on the page that give you other helpful information.
Anyway, spend some time to think about this and assemble a workable emergency kit.