I did this all of last year, and this is what worked for me:
1. Limit the range of ingredients you use. Make a list of everything you need to have in the house at all times (salt, milk, bread, cheese, flour, toilet paper...). My list is two two-columned pages with headings such as pantry/fridge/freezer/cupboards/bathroom. It takes ~10-15 minutes to go through it all and make a shopping list for the week.
2. Add the ingredients for what you plan to cook that week to the list. Go to the store only once a week. Go to the fewest stores you can get away with. We go to ALDI and a local grocery store, and that's it. What they don't have, we don't use - again, limit your options. A few times a year, we go to a local Walmart to get stuff ALDI does not have. It takes ~2.5h to do the shopping, unload the groceries, and put them on shelves in proper order (newer stuff in the back, older stuff that expires sooner in the front). You only do this once a week though.
3. Cook only 3 dishes per week. Rotate the dishes through weekdays: A,B,C,A,B,C, and Sunday it's either leftovers, or something's happening (people coming over, us visiting friends...) that takes care of that day's meal. I made sure one of the dishes is vegetarian every week, just for health and variety (and maybe cost).
4. Cook all dishes at once. Use a slow cooker. Have more than one set of pots. It takes ~3h or less to do all the prep and then stuff is cooking while you do other things (laundry, work on a laptop in the kitchen...). Some things will need to be stirred, some can be left alone for a while.
5. Make a variety of very simple dishes. It was very important to me to not cook the same thing over and over again.
6. One type of endless variation is protein+side vegetable+starch. Protein can be chicken/turkey/pork/beef/fish/eggs/tofu/edamame, prepared as roasted/stew/sausages/sauteed in pan w/ spices/breaded (prepped,frozen) then roasted/steamed, all with or without onion, garlic, and/or variable spices if desired. Vegetables can come frozen and microwaveable from ALDI (I make those the day of). Starch can be bread/buns/naan/pita/tortilla/mashed potatoes (made the day of, instant or 'real')/various grains/rice (brown, white)/corn (frozen)/noodles/dumplings. Endless combinations. This is very handy when you have people over.
7. Another type of meal is a bit ethnic and involves beans/green peas/lentils/etc. cooked as a big pot of, let's call it, soup. Add onions (sauteed first is best), garlic, cubed pork/beef (or not, legumes are protein), sometimes carrot, sometime peppers, salt, pepper and cook until it's cooked (usually ~45 min). Add dill to green peas. Serve beans with crushed pepper (spicy) and/or crumbled feta cheese. Serve lentils or green peas with plain yogurt or sour cream or fresh lemon juice or vinegar. To thicken, add a cubed potato (not too much).
8. To add to variety, cook other ethnic dishes such as mousaka (potato/zuccinni/egglant/all of the above), stuffed peppers/eggplant/tomato. These can be made in big batches and frozen for later. Try paprikas. Stews can be served over noodles or dumpling. Etc.
9. Carrots can be cooked with onion and meat, ditto for cabbage with cubed meat or beef sausage (cooked with cabbage). Frozen mixed veggies can be cooked as a vegetable soup. Go easy on water, add salt and pepper or other spices, stir in lots of sour cream after it's cooked. Use canned soup as a pre-meal to a more solid/meaty dish. Frozen, cooked meatballs can be bought (ALDI has turkey, Sam's has beef) and cooked with a couple of cans of crushed tomato (add Italian seasoning).
10. Occasionally cook Italian: any of the many types of pasta with any of the many types of pasta sauces. Combine. For variety, you can fry some chopped onion, then add ground meat on top, fry cook, then add pasta sauce. This works great with marinara and other red sauces. Frozen pizza (cooked day of) can be healthy (ALDI has a good variety if you catch it).
11. Occasionally cook Mexican: ground meat can be cooked with spices in a big batch, then served with tacos or tortillas. Veggies on the side. Beans optional.
12. Occasionally cook Asian: ALDI sells frozen stir-fry bags (veggies and chicken/shrimp) and similar. These are made the day of.
13. Use plenty of onion, sauteed, chopped or thinly sliced, as a base for cooked meals. Ditto for garlic (to taste).
14. Always have hard boiled eggs on hand. When in doubt, microwave frozen veggies and serve with eggs.
This may not be what you are looking for, since these are not exact recipes. But that's a feature, not a bug. Dishes are simple to cook, simple to remember, simple to look at - nothing flashy. Many do not have a name or specs, they are just healthy food. You can be a bit off with cooking, but it's still the same dish. You can vary to your family's tastes. Better yet, since you may be discovering some dishes for the first time, you get to form your family's tastes. Better yet, these are easy to teach. You can involve your child in the preteen years, and by college time, they will be able to feed themselves well and cheaply.
I call this survival cooking. When my youngest becomes a tween, I will branch out into fancier cooking, entertaining, pastry, deserts, homemade whatever... For now, my time is limited and better used elsewhere.
