I'm with Hick.
If on foot evading and making a tactical movement, stealth and mobility are key. Anyone carrying a long gun has a distinctive silhouette which can be identified as a potential threat with binoculars from well over 1000 yards and at minimum is going to be observed and tracked, so your cover is "blown." You can maintain situational awareness while giving the appearance of a hiker or timber cruiser without screaming "mall ninja!"
Personally, I would avoid having to bug out on foot. A folding mountain bike is best if you must leave your vehicle. If moving with the family multiple bikes make sense, especially with small children. I would carry my normal EDC handgun capable of .38 Special +P or 9mm minimum, and have a second pistol or revolver of the same caliber, but having a longer barrel for improved sight radius, ballistics and hitting ability, which could share the same magazines, and which you have practiced with out to 100 yards or more. Having two handguns enables you to arm the spouse if she doesn't routinely carry her own. When I was growing up in the DC area during the Cuban Missile Crisis, Dad made sure that we kids all knew how to use the DCM M1 carbine (which I still have). My older brother was schooled on the M1911 .45 and Mom carried an S&W Victory .38 Special. (I still have them too).
Today I routinely carry a 6-shot S&W Model 10-5 snub on my person all the time, and have an extra 4-inch .357 revolver in the truck or car ruck. Basic load for the snub is six rounds in the gun and two speed strips concealed in pockets. The Ruger Service Six or S&W 28 Highway Patrolman ruck gun, depending upon which vehicle, has six .357 rounds in it, two speed loaders of same and an extra box of .38 Special full-charge wadcutter handloads which can be used in either gun, their purpose being primarily as hunting ammunition and to conserve the personal defense loads. In warm weather there will be a Speer shot load first up in the cylinder, and one in each Speed strip reload, as well as a box of 10 more shot loads in the ruck. This same ammo load-out is well proven for camping and fishing trips up to ten days or two weeks, because unless actively hunting for the pot (which you will NOT be doing in an E&E scenario) you will very seldom fire the gun. Ideally you will avoid shooting at all if you are stealty in your movements, practice good field craft and don't do anything stupid.
I regularly practice out to 100 yards with my revolvers. The expectation is to hit an IPSC Item target 4 out of 6 times with the 2-inch snub, and 5 out of six with the 4-incher, firing from a two-handed, supported field position. Certainly adequate for suppressive fire, "shoot and scoot." If you are unable to do this after practice, then consider an M1 carbine or handgun-caliber lever-gun. I say this because the distinctive silhouette of an AK, AR or other EBR "scares the natives" and commands unwanted attention which an ordinary "agricultural" working gun does not.
In the words of the late Harry J. Archer, "if you stand and fight you'll never live to shoot'em all...!"