Even though this thread is 3 years old, the subject matter is still valid.
My kit is pretty light and I carry it in the vehicle with me at all times.
I have a tarp (blue plastic, 9x11 for shelter or I can make it into a litter)
woolen blanket (warm even when wet, won't be destroyed if an ember hits it like synthetics)
50 gallon heavy garbage bags ( usually 4 as theywork for multiple purposes including extra clothing, sleeping bag, rain gear, water collection etc.)
knife (in addition to the 2 I usually carry it is a heavy fixed blade, and one I made out of carbon steel so it works with a flint to start a fire)
folding saw
firestarters/tinder (mag match, fire piston and zippo lighter and a few kitchen strike anywhere matches, my tinder is a old chewing tobacco can with cotton and vasaline in it)
candles
wind up flashlight
snare wire and a couple fishhooks and some line
paracord
multi tool
black electricians tape, (works a lot like duct tape, but smaller and easier to carry)
small pot/cup for cooking
water purifier (iodine)
and some bullion cubes and protein bars for emergency rations.
extensive first aid kit
Extra socks/skivvys/gloves/wool cap/long handles and a light but warm jacket.
a referees whistle for emergency communication or calling for help.
A steel mirror (for signaling and also works for starting fires)
The wife's pack is pretty much the same, with a couple added things for ladies
I agree with Submariners choices, but the current situation is that 22 ammunition is nearly impossible to get, so I would go with a more widely available cartridge like the 30-30 Winchester for the rifle.
410 is a good choice for small game, but a 20 gage is more versatile for larger waterfowl as well as small game and upland birds as well as self defense. A single shot gun works very well. I would also go with a shot size large enough to take the local game, but not so large it would rip up the small game.
I am not a huge fan of the combo guns, but they are out there and do work.
Combination gun - Ask.com Encyclopedia
My main argument against them is the fact if you break your weapon, you only have one and you are SOL no matter how much ammunition you have.
I know the country I am in intimately as I spend a lot of time in the outdoors, I carry what I use so I don't need a lot.
My bug out bag is set up for indefinite stays in the wild, but I carry enough so that even on foot I could cover the ground necessary to reach one of my backup sites within a few days.
If you have a plan in place you can make your plans of what you need to have in your bag to get to safety, or survive for a period depending on your situation.
For example, there is a place not far from where I live with a lot of caves, (shelter), and lots of rattlesnakes (Food), and a river, (Water and more food). Firewood would be the main problem, but there are a lot of shrubs around there and if I have a good cave, I wouldn't need as much wood as I would if I were in an exposed position.
Make your plans of where you would go, then you can make your bag up accordingly.