The format is fairly standard for a "reality documentary". It does go with the more extreme folks rather than the more common folks who are just putting some things aside for rougher times. But that's OK, in most of the cases. I found many of the people to be pretty ingenious in how they've approached what they perceive to be The End Of The World As We Know It. Maybe they're right, maybe they're wrong. A few might even be slightly over the top (well, there are a few that I think put a step ladder on the top and went from there...) But they have what they consider to be valid reasons for doing what they're doing, so who am I to argue?
Somewhat counterintuitively, saving money is not just about cutting down expenses; seeing a higher balance on a checking account tends to instinctively make us less frugal, too. To counter this trend, I found it helpful to set up a small, daily transfer to a savings account, in an amount that blends in with daily purchases - say, $10 or so. This method takes much less planning and mental discipline than trying to make one big deposit every month. And hey - when you are comfortable with $10, you can painlessly test the limits by gently ramping the amount up.
I hope this makes sense to you. It sounds like you have already figured out that with a growing teen and two additional children in the household, this will be a good start but that more will be needed over time. By doubling these quantities my guess is that you will be better prepared, food wise, than 90% of the population. And even without doubling the quantities, you will be better prepared.
No heating in the middle of a particularly nasty winter can be problematic, too - although it's mostly a matter of comfort, not survival. In most places, with robust shelter and adequate clothing, bedding, and food, it's fairly hard to freeze to death at home (but note that the cold may make some infections or medical conditions worse; you may have to worry about frozen water pipes, too). The situation can become a lot more dire if you are on foot in the middle of nowhere, so truly hardcore, wilderness-minded preppers may have something to ponder about; but hauling a sufficient amount of fuel is typically impractical to begin with, so their best bet would be warm clothing, improvised shelter, and the ability to build a fire. We'll talk about that in the section that deals with camping supplies.
Survival kits, in a variety of sizes, contain supplies and tools to provide a survivor with basic shelter against the elements, help him or her to keep warm, meet basic health and first aid needs, provide food and water, signal to rescuers, and assist in finding the way back to help. Supplies in a survival kit normally contain a knife (often a Swiss army knife or a multi-tool), matches, tinder, first aid kit, bandana, fish hooks, sewing kit, and a flashlight.