Tough questions! Here's what I'd do:
Gun: Remington 870 12 gauge; 1 box buckshot and 25 rounds of slugs. (50 rds total) This will take care of close and intermediate "threats" (out to 75-100 yds anyway), allow me to hunt and also it is a gun that simply won't jam/break down on me. I can take it down and reassemble in the dark, and can carry it all day pheasant hunting, no weight problem for me. (I'd take the plug out of the magazine on the way out the door). SECOND PLACE would be my Red Rider BB Gun with a compass in the stock and a thing that tells time.
Lighter for sure (hate to eat raw meat), fires are nice in the evening
What to take from the house? Just one thing, it would be a hunting knife. If more than 1 thing, a backpack w/ some bottled water, extra socks and underwear, cellphone
leave the cannoli - take the gun