Growing your own, (including chickens) and preserving your own or seasonal gluts from shops, are both really good ideas.
Personally, I looked (years ago now) at what we normally eat, and have some extra shelf stable versions of those in my cupboards. Plenty of seasonings (that I rotate through as they lose flavour) as well as basics.
If you are very worried, think not just about tins of beans chickpeas lentils etc (that you would use anyway) but maybe also getting 1 bag of dried versions…try these out and see if they work well for you, then maybe get a second bag.
Look around for tins of things you would eat…like where I am, I can find tins of clams, mussels, confit duck, hotdogs, coq au vin, cassoulet, tuna, corned beef etc. some are very expensive, some very cheap. No spam or tinned chicken. I don’t buy all of those, but I have a handful of ones that I will eat set aside. When I use one from my stores (or the week I plan to), I will buy a fresh one to replace it. Or if there’s a special (the French meals sometimes have seasonal specials), I will plan to use my older ones and replenish.
The same with veg. I normally have a lot fresh, some frozen (and some I’ve frozen). But I have a choice of various kinds of beans, peas, carrots , corn, mushrooms, potatoes, asparagus, bean sprouts (expensive!), water chestnuts (very rarely and expensive), olives, ratatouille etc in tins or jars. So again, I keep 5/6 extra tins of veg I will eat and replace them as I use the older ones.
and I usually keep at least 1 spare of each type of carb I use (couple of kinds of rice, couple of kinds of pasta, couscous, bulgar wheat) and also of corn flour, regular flour and other baking items. If you have space, and can store them properly (sealed in food safe containers away from bugs, may need oxygen absorbers, etc), you could have a bit more.
The most important thing is to only store what you and your family will use, store things properly, and rotate to use up older things before they go off (not just ignore the “long term stores” while you do weekly shopping and cooking).
Preppers board here may be useful, and YouTube has some great resources too for storing food properly.