My husband is on the Specific Carbohydrate Diet (SCD) for his Crohn's, and eats largely meat, cheese, and some fruit and cooked vegetables. Stocking up food for him is hard!
We usually have a month's worth of cheese in the fridge, and that amount of meat and frozen berries in the freezer, but those require refrigeration. Here's some of the shelf-stable paleo/SCD/GAPS food we store (not all may work for you, and some are pricey!)
- Canned fish & other canned meat
- Lorrissa's Meat Sticks (these don't have anything funky in them--just meat and some herbs. We found them at our local grocery outlet store for really cheap and bought all of them. Now we buy them for an arm and leg at Amazon because it's one of the few foods my husband can easily eat)
- Moon Cheese These are just baked, dried cheese. They're a snack he can eat. They also cost way too much when we can't find them at Grocery Outlet (we buy all of them when we find them at Grocery Outlet)
- Dried fruit, like raisins. We also dry our own peaches and apples. This probably won't work for you, though
- Canned fruit (probably won't work for you, and are pricey. We could can our own, but life has not afforded me that time)
- Canned cooked beans (This likely won't work for you, but my husband can eat them in limited quantities. Soaking and preparing my own beans would be better, but I never manage to do that)
- Dried medicinal tea ingredients (mint, Oregon grape root, quercetin, turmeric, ginger, green tea, yarrow). We don't want to run out of these when he needs them. I try to dry as many as I can from our own property.
- Nuts (he can only eat a few, but it's a nice supplement/snack)
And third is that when we have canned meats on hand, those tend to get eaten quickly, especially if my back is acting up, because it's easier to open a can than to cook. So I need to think about how to do this.
I'm currently of the mindset that this is the sort of thing I'm preparing for. It's like a minor disaster. We need to be prepared for the times we can't cook (because life is too busy or our health is too bad). My kids just eat gluten-free & organic, so I try to keep some organic, gluten-free frozen pizzas and burritos and mac & cheese on hand for those when there isn't time to cook. And, because those (A) Cost more, and (B) Aren't as healthy, I make myself cook dinner whenever I am able. I save those "convivence foods" for our "minor disasters." My husband's meat sticks and Moon Cheese fit into these categories as well. Most of the time, I try to cook steak or eggs or ground beef or some other meat for him. But, it's hard to do that for breakfast, lunch, and dinner--especially since we both work. So, I have to be okay with spending a bit more to have food he can just eat without cooking or refrigeration.
I guess what I'm saying is, if your finances can afford it, don't stress about eating easy, canned food when life is hard. You need to eat to stay healthy and care for you and your kid(s). Part of the prepping is cooking dinner when you're able, so you can eat the canned food when you aren't able to cook.
Five acres, two little ones, one awesome husband, 12 ducks (give or take), and a bunch of fruit trees and garden beds. In her spare time, Nicole likes to knit, paint, draw, teach kids, make fairies & dragons, philosophize, and read fantasy. She doesn't HAVE spare time, but does like to fantasize about it! 
