A flintlock muzzleloader in at least .50 caliber might do the trick.
In a modern cartridge gun, I might pick an H&R single shot in .223. Overkill for rabbits and such, but it will kill most things, and be easy on weight and cost, both for the rifle and the ammunition.
A Lee-Enfield would do as well, especially a US 1917 chambered in .30-'06 for ammunition availability, as would many other surplus military weapons, such as a Mosin Nagant with a couple of cases of ammunition laid in for very little money compared to other centerfire rifles.
There are any number of people who will pick the 12 or 20 gauge shotgun for its versatility and terminal effectiveness. The ammunition weighs a lot per round, but anything you hit is usually done, if you used the right load and can shoot. I can see that, and in fact, for hunting, my shotgun is my most used gun, simply because bird seasons last so long around here compared to anything I normally hunt with a muzzleloading or centerfire rifle. An H&R single shot, a Remington pump, or many others are long-lived enough here.
Probably an equal number will pick the .22 LR for its weight, accuracy, and cost advantages in feeding, not to mention quiet harvesting of game. I can see that argument as well, but it lacks something in its effect on bigger animals. Survival means, yeah, you might have to do something to kill a deer that you wouldn't normally do, so you can eat, but it's been done before, and will kill them -- brain shot, especially. But it has limitations on range, and terminal effect on things intent on hurting you back, so ... it's a judgement call for your area and the needs you might face there. Ruger 10/22, Marlin 60, or a bolt action, or ... basically, pick your favorite and put it to work.
I might pick my AR15, in spite of your "no assault rifles" rule. Survival can mean more than hunting, and a similar rifle helped me survive for a year when it was my best friend. If you've slept with a rifle in a combat zone, you might have similar feelings about that weapon.