Real Food On a Budget

At the first glance, this seems like a very expensive plan.  It's actually the opposite.  Real food is considerably less expensive than processed food.  I've managed to do it in a country known for a considerably high cost of living, and spend about 2/3 of what I used to on groceries.
 
An example, a jar of a good quality mayonaise here costs about 15 NIS.  A jar of tahini paste costs about 20 NIS.  However, for that one jar of tahini paste, you can make the equivalent amount of dressing of 3 jars of mayonaise, and avoid eating any hydrogenated fats or artificial flavoring.
 
Another example is breakfast cereal.  A box of a relatively good breakfast cereal here costs around 25-30 NIS for a 750 g. box.  A dozen large regular eggs costs around 14 NIS.  An entire 1 kg. loaf of full rye bread costs 15 NIS.  Fruits and vegetables in season are usually around 1-3 NIS per kg.  You could feed your kids an egg, a piece of fruit, and toast or oatmeal for less than boxed cereal and nothing else.
 
Just don't buy unreal food.  Buy meat in bulk once a month unless you have a deep freezer.  If you do, try to get red meats in their best season, and chicken when it's on sale.  One adult eats 4-5 kg. of meat per month, so budget with that in mind.  Also, since you're not avoiding animal fat anymore, you can save big by buying the fat other people don't want.  Chicken skin is dirt cheap.  If you are on a really really tight budget, you can supplement smaller amount of meats and beans with the fat others would throw away.  Most butchers are happy to sell you their leavings because there are so many that even they and their families can't eat it all.
 
Another neat way I've found to save money is to buy dry salami.  When I find butchers and smoke houses I trust, I buy any sausages I need from them.  Salami is usually full of salt, so it's an occasional indulgence that if I'm going to have, I have the good stuff.  The good stuff is always dry-able.  You hang it up, wrap the bottom with a paper towel or absorbant cloth, and cut it as you go.  It's also great for flavoring soups and porridges.
 
Different countries have different customs and schedules for slaughtering, but generally lamb and pork are done in the spring.  Lamb needs to age 5-6 months in the freezer.  Red cuts of pork should also age, but white parts are good fresh.  Beef is usually slaughtered in the winter when temperatures are just around freezing.
 
So the best way to buy meat is as close to the source as possible.  If you don't have a deep freezer, this will be a butcher who buys direct from the slaughterhouse.  If you do have a deep freezer, it's best to buy directly from the slaughter house.  Even better, get together with a group of friends to buy a bulk of meat together.
 
Dry staples like beans, nuts, and grains should be bought in bulk and properly stored.  Much food is wasted that goes stale or gets infested with bugs.  Invest in some good airtight containers.  Sometimes though, the best containers come from the same place such things are sold.  If you can, get rice in unopened shipping bags.  The smallest I've seen of these is the 5 kg. bag that is made of a coated woven bag over a dual layer plastic bag.  Whatever you get should be what you and your family can eat within 2 or maybe 3 months.  For a small family, it's best to have a relatively fast turnover because sometimes despite one's best efforts, little critters get into the stuff anyway.
 
If you are having really hard times and have no time to shop for fresh vegetables, you can get by on inexpensive dried storable green foods like split peas, parsley, and seaweed.  Many kinds of greens also grow wild like dandelions, mustard greens, and polk salad.  Take a stroll through a vacant lot with a basket sometime.  Just make sure you know what to look for, and what you're getting.
 
Many large grocery stores have a problem with selling what are normally scraps and discards, and things close to their sellby date, but many smaller and smarter ones don't.  Talk to them about what they do with odds and ends, and find out if you can get their cabbage, cauliflower, broccoli, turnip, andd beet greens.