It may sound stupid given all the great choices out there, but if I had to pick one gun, in an "end times" scenario (yes I know this is a bit OT) I would pick a sporterized .303 Lee Enfield. It'll knock down anything in NA, simple mechanically, lots of spare parts, brass will reload quite a few times and just generally tough as nails.
Now more on topic, if I were to pick a rifle to take to the grave in our current low stress environment it would either be a Winchester M70 in .308 or a Remington M700 in the same caliber. Stainless barrels, McMillan or B&C stock, 3x9 Leo scope plus iron sights just in case the scope gives up the ghost. I'd hang a bipod off the stock as well. Not ###y but gets the job done.