In any situation your best weapon is always your mind. there are so many possible scenarios when the SHTF that each must be addressed seperately.

Situation 1) You are home and planning to stay yet gangs roam the streets looking for easy pickings:
This is where a 12 gauge shotgun is incomparable. Street sweeper with pistol grip or a Saiga 12 gauge with ammo drum. Any pistol larger than 9mm would also be great. Load with 00buckshot and its hard to miss.

Situation 2) You've abandonded your home and gone off into the woods.

As many have mentioned a Ruger 10/22 is a great choice. It's cheap, reliable and very accurate out to 60 yards. A 4x scope will bring home the squirrels and rabbits. You can't easily kill a deer with a 22 but you can stun them with headshots until you can get close enough to finish the job. Same goes for people if they insist on coming after you.

PORTABILITY and the number of rounds you can carry make the .22 a very good choice for woodland survival. Gun and 1,000 rounds weigh about 15 pounds. .22 tracer rounds are also available as well as subsonic ammunition that is relatively quiet.
I would also carry a semiauto 9mm or .45 with an extra clip and 100 rounds for a little more serious firepower.
Those who believe they can tote around a Barrett .50 will find out really fast it was a bad idea.

If you have a partner I would suggest one carry a good rifle while the other totes the .22. -this would give you the best amount of versatility.
My choice of rifle would be an AK47 if youre worried about people with hostile intent. I wouldnt care to get into a firefight with a bolt action rifle although the bolt action 30-06 or winchester .300 are good calibers for hunting large game. mauser 8mm is also a great surplus rifle than can be had for cheap. Also on the cheap, the SKS is about the best value you can get in a semiautomatic rifle. it's ideal for women and children as the stock is very short and the gun itself is relatively light.

If they get past whatever bullets I can send their way then I'm a sitting duck. At 5'6" and 120 lbs theyre pretty much gonna take me down. lol