If you have never heard of the foxfire books please look them up online and read 1-5.What they are is a collection of stories wrote in the sixties by high school kids talking to their grandparents great aunts and uncles about life in the Appalachian Mt's.Most of the books are first hand accounts of things that had to be done to just live a lot of how to a lot descriptions of there daily life.If you do read the books remember they had no electricity no cars few stores and little money.
I have a lot of respect for the abilities of the people in these books .When i read books of this type i look at modern things that we have available for off grid living today vs back then.Our modern mountain families even if they are off grid and living off the land have it so much easier than the folks in the 1800s had.By the same token people from back then knew more about what it took to live that kinda life.If i had to live off the land with only 1 modern item i think i would pick a chainsaw.The amount of time they took with falling trees and making lumber and usable items was huge.A chainsaw would free up a lot of time for other things.You may wonder why not a truck? No roads .Solar panels ?Why a lantern was available and candles.Guns yea modern ones would be nice but black powder was OK and it wouldn't save time.A fridge? No i have waded a mt stream its plenty cold for milk and most food .So i am back to the chainsaw.Even with a good chainsaw falling cutting and splitting a cord of firewood is a lot of work.Could you do it using a 2 man saw bucking horse saw then split it?
If something happens and we devolve back to this level read these books and choose what you could do to make it as manageable as possible.For me a chainsaw is my pick i have 3 and 10 gallons of Coleman fuel for long term.I also have a 10 gallon ethanol generator (a still) that i have used for many years.What do you think your 1 item would be for you.