I hate to disagree because, I do enjoy my 22s. But if every thing does go to hell, where are you gonna get ammunition for a .22. Reloading rimfire ammunition is not an option. I think the old guys out west 125 years ago had the right idea. What will be needed is a center fire handgun and rifle chambered the same. While I am partial to .357 Mag/.38 Spec, there are other rounds that are effective. There is reloading equipment available that will fit into a fairly small container.
I have rifles and pistols up to 45/70 but I really like my .22LR and .22 mag firearms. I have a Contender in .22 mag (10” bbl). I also have .44 mag and .30-30 Contender pistol barrels.
Also, don’t forget airguns. A good gas piston springer in .22 will work for small game and the precharged pneumatics will work for medium game. I have a .25 pcp that is very quiet and rivals a .22LR.
Great resource: Jim Chapman’s Practical Guide to Airgun Hunting - http://www.americanairgunhunter.com/2ndedition_PGAH.html
The solution is to stock up now. .22 ammo is relatively cheap, and makes good trading material. You can buy 6000 rounds of .22 ammo for the cost of a simple reloading outfit.
Not that I disparage reloading, but the cost of a primer is more than the cost of a .22 cartridge.
I have reloaded many thousands of rounds of ammunition over the last 50 years, but it is very hard to beat the utility and cost of .22 ammunition.