A lot of different ways stuff can go bad. Having a handgun, shotgun or rifle available can keep many of them from doing permanent harm to you and yours. Trying to figure out just what SHTF scenero to be prepared for is a crap shoot.
Handgun: can be with you always. Is a wonderful equalizer that 19 out of 20 times prevents escalation to violence. I don't know when or who would deliberately challenge someone facing them down with any handgun - even the sub-defensive calibers, though I wouldn't carry less than 9mm and personally prefer .357-auto. But I also carry an unloaded AK-47 and 5 loaded magazines in a bag behind my pickup seat.
Rifle: has a lot more power and distance capability. If the situation justifies shots beyond 50 feet, the rifle is the best choice. Rabid dog, 4-legged preditors or 2-legged preditors, the rifle is probably the best choice. However, there aren't many scenereos where a normal guy is going to feel justified at killing people at 100-yard or greater ranges. I think the SHTF rifle to be parked in your vehicle should be inexpensive, have large magazine capacity and doesn't require .308 or 300-mag ballistics nor long-range scopes. However, there are places I visit where I have to remember to trade my "evil" rifle in for my shotgun.
Shotgun: is the best intimidator and for 10-50 yard defense is probably the best choice. With 000 - #7 shot it is a lot safer in populated areas than rifle bullets. If I'm standing down a gang of thugs, I wanna be holding my Mossberg 590 special-purpose (20" unchoked, ghost-ring, 8-round tube). When I visit my old Kalifornia friends, the Mossberg in a bag with a bandoleer of slug-00-04 shells replaces my carbine.
Odds are I won't need to forcefully employ any of these in my lifetime. Having them nearby is good for my emotional health - just a few less things to worry about. I also carry extra clothes, food and other tools that I don't expect to use. Guns are no different. Guessing what to carry is just that: guessing. But we can try to make thoughtful guesses.
P.S. regarding "assault rifles": Can't we, in the shooting community at least, agree that "assault" is a behavior and that guns do not have behaviors? Semi-auto carbines are just another type of gun. They do not animate themselves or attack anyone. Assault rocks, assault bats, assault golf clubs and other applications of the anti-gun-coined adjective are ridiculous. Let's not give the Brady Bunch the advantage of modifying our language.