I don't have a survival hideaway in the mountains, so I guess I'd have to pack a tent and my backpack, and plan to escape and evade until I found allies or a good place to settle.
A 12 gauge shotgun would be tempting, since it is indeed a good all-purpose gun. Small game, deer, defense, etc. Carrying lots of shotgun ammo is something of a problem if you have to abandon your vehicle and take to the hills on foot, though. Being "on the run" and therefore lacking a smokehouse or refrigeration facilities, killing a deer would seem a waste, anyway. It takes a heck of a lot more time and energy to find, kill, and butcher a deer than a couple of squirrels, rabbits, wandering dogs and cats, etc. Hunting these little guys enables me to eat and run.
So I think I'd actually take my scoped Marlin .22 and oodles of its easy-to-pack ammo. I can take all manner of small animals with it. It is very light and easy to carry while I'm using my "ninja-like" bushcraft skills to avoid whatever calamity has forced me into the woods. It has a fifteen round capacity, and is easily capable of ocular-cavity shots on human targets at 75 yards. At closer range, I can hose unarmored bad guys with 3-4 shots each, which will probably discourage them. The muted report of the .22 doesn't carry far, and will enhance my hiding abilities, too.
Would I choose this little gun to fend off the Mongol hordes or the blue-helmeted oppressors? Of course not, but having seen light infantry squads in action, I wouldn't try that with an AR or an AK either. In the immortal words of Monty Python, "Run away!" (If they really want you, they'll run you down with a chopper. Nothing short of a deep cave -- and certainly not a puny little .223 -- will save you from the hell an attack helicopter can unleash.)
I'm also with Tamara on the handgun question. My .45 auto is holstered on my person when I am awake, so it would naturally accompany me as a short-range defense gun.
Mike