I am curious; how would you modify or equip your 10/22 for SHTF duty?
1. 16" barrel - .22lr doesn't gain any steam after this length due to the tiny amount of powder, and longer barrels can actually slow bullets down. The barrel diameter doesn't matter, it's the chamber cut and crown that count for accuracy. You can have a stock barrel rechambered and recrowned and it will shoot as well as the expensive aftermarket choices. If you want aftermarket, Green mountain sells heavy, fluted 16" barrels for less than $100.
2. A lightweight, but rigid stock. There are tons of choices, but most options for the 10/22 are pretty cheap. The Hogue overmould is one, it is just too floppy, and that stupid sticky rubber coating is like glue to dirt and other crud that I don't want stuck to a weapon. The most inexpensive stock I'd go with is a Fajen, they're made from harder polymer and cost something like $60. The "folders" aren't even an option for something that will be relied on, they just don't allow a decent cheak weld to place shots properly.
3. A quality scope with sturdy rings. Many of the scope bases for the 10/22 only allow use of 2 out of the 4 mounting holes. I would find a 1 piece base that has 4 screw holes and use quality rings (cost more than $10 and not sold at Walmart). I would also spend at least $100 on a scope, but shop for something paralex adjusted for rimfire ranges. Weaver and Leopold both make decently priced "rimfire" scopes that are great quality.
4. Trigger work - the stock trigger is just too rough for any real accuracy, and pushing a rimfire to its limits requires exact shot placement. There are numerous action kits, but some of them require minor gunsmithing to install.