So, this is no joke. I loaded the Mini-14 with ammo labled "Lake City M885". The tips have some kind of green coating.
That should be M855. That is current mil-spec ammo and is your #1 choice if you're going to use your Mini-14. It is 62gr FMJ with a steel penetrator tip. It will do as well on cars as anything in .223 will that you can realistically get*. As Lake City ammo it is the same as what is used by the US military and should be high quality, at least in terms of reliability. (Accuracy is not there with match ammo, but will be as good or better than your Mini-14 will shoot.)
[* the military may have access to M995 AP ammo with a tungsten penetrator. I don't think this is in much military use and I'll be astonished if it's available to civilians.]
You're in a terrible situation and honestly I'm really glad I'm not there. Of your current choices I personally would use the M1 Garand, with as many 8-rd clips loaded as I had available (or at least 10-15 if you have dozens of them).
But, if your situation possibly allows, I would get either a .308 battle rifle, or a semiauto 12ga shotgun with as much capacity as possible, and loading 000 buck (8 pellet each).
On the shotgun side, a Saiga 12 would be your best choice - good luck finding one. Runner up would be a Mossberg 930SPX, FN SLP, Winchester's tactical model (same as the FN), or a Remington 1100 tactical.
On the rifle side, any of: PTR91, FN-FAL, AR10 (including LAR-8, DPMS model, SAR-25, etc.), or a Saiga .308, again if you can find one. CDNN is in Abilene and has the PTR's at a good price. I don't know if they have a retail store, but they could certainly ship to your local FFL quickly. Any of these would compare well to the BAR, though aren't as heavy. I think the Saiga, PTR and FAL would be tops in reliability, and among those I'd choose based on price and availability.
Before seeing the test results of 000 buck on sheet metal and gelatin I would have chosen the rifle, but after seeing those the shotgun looks pretty compelling.
I would have all responsible family members armed with a rifle or shotgun at all times. The Mini-14 would be perfect for someone who can't manage the recoil of the bigger stuff.