I am a type 2 insulin dependent diabetic, and have used several methods for storing insulin, both for routine day to day, during power outages, and travel, both by car and airplane. Here is what I do:

Refrigerator: pretty much everyone's starting point.

Short local travel: Frio wallet (no association). Works reasonably well, holds a pen and a vial (I use both), but that is about it. I have been told that in an emergency, wrapping insulin vials and pens in a wet towel kept in the shade will produce the same evaporation cooling effect, thus allowing storage of more vials/pens. I also have a supply of freezer packs in the freezer (I get them "free" as my insulin is shipped to me in styrofoam containers with cooler packs.)

Backups at home: For many years I used a small generator to power the fridge, then later went with a auto standby generator.

Long auto trips: I have a small 12 volt thermoelectric cooler that doubles as a standard insulated cooler when not powered.

Airline travel: The hardest. Always take all medications and supplies in carry on. As for the insulin, I have one of those insulated lunch bags, and put my pens and vials in a plastic bag surrounded by thin bubble wrap, then one of the freezer blocks, surrounded by regular bubble wrap, and then into the insulated lunch bag. Never had a question from TSA (keep everything in the box they came in with the prescription on in). I have found that this setup will last about 20-24 hours before the freezer block has fully defrosted, but everything is still cool.

I have no experience with off the grid/disaster storage, but I think you should plan on having several options if you can. I took a quick look at the sites Dagny listed and saw one technique that look very interesting----the deep hole in the ground. A variation of that could be as simple as a cool basement.

Hope this helps.