A 3 month supply of foods you normally eat gives you a good supply in case of strikes, pandemic, bad weather emergencies, job loss, and many other emergencies. It is a convenient way to cook, having to run to your food storage room for an ingredient rather than running to the store. It is also economical, since you can stock up when something is on sale, then eat at that sale price for some time, hopefully until it is on sale again. For example, my mother-in-law used to buy one can of tuna every week. I would buy a case when it was on sale, and save over half the cost that she paid. The trick is coming up with enough money for the first case. But if you start doing more cooking from scratch, and eating out less, you can save enough money in a short amount of time to pay for a case or two, and then it will just snowball.
So how do you decide what to buy? My favorite way is to work out a menu of meals your family likes, which can be made with shelf-stable foods. That doesn't mean you always have to make those meals with shelf-stable foods, just that you can, and you use those shelf stable foods in that menu or another recipe often enough to keep your foods rotated. For example, when I make spaghetti with meat sauce, I normally use hamburger from the freezer, but I have some home-bottled hamburger I could use if I need to. To rotate the jars of hamburger, I could use it in spaghetti, or any other recipe, on a day when time is short. Oh, and when you buy them (or can them), label your cans with the date, so you are always using the oldest food first.
For a 3 month supply, it is easy math-wise to make a menu for 10 days. Multiply the items needed for each meal by 10, and that tells you how much you need to buy to have a 3 month supply of food. Of course, this is a very individual thing, because each family has their favorite meals, or different dietary needs, etc. That is exactly why you won't find a list telling you exactly what to buy for your 3 month supply.
Once you have planned your menu, go through each meal, and tabulate how much you need of each ingredient. For example, for spaghetti with meat sauce, I would need spaghetti noodles, spaghetti sauce, and a pint of hamburger. I would add a pint of green beans for a vegetable. So for this menu for 3 month, I would need 10 packages of spaghetti noodles, 10 cans of spaghetti sauce, 10 pints of hamburger, and 10 pints of green beans. Do that for every meal you are planning. That will give you a shopping list of what you need for a 3 month supply of food. To make it easy to calculate, I just figure that the recommended amounts for the 1 year supply of long term storage will basically give me a loaf of bread a day, if I add yeast, baking soda, and baking powder to my list. That saves adding up lots of teaspoons of things, even though it isn't as precise. I figure I will do easy, I may or may not do complicated. lol I also don't plan a lot of variety for breakfasts and lunches, which also simplifies planning.
Of course, there are other ways to come up with your list. Some people just like to buy extras of what they buy every week. If you buy a fairly standard list each week, that should work for you. Others like to put a date on when they open something like catsup, and note when it is used up. If you use a bottle of catsup in 2 weeks, then you would want 6 or 7 bottles for your 3 month supply.
I don't include frozen foods in my food storage inventory, because it is so easy for a power outage to occur and ruin all those frozen foods. Some people prefer to include their frozen foods, it is a personal choice. Anything you add to your food storage will give you that much more security. I have enough food storage that now I mainly buy fresh stuff, stock up on things I have used that are on sale, and maybe get a few treats. When DH lost his job, we cut our food budget about in half, and after 16 1/2 months, we are still eating like normal. It is worth the small amount of work required to develop the supplies to enable you to go for a time on limited access to the grocery store, or even to skip the store altogether. Best wishes.