To start with, my advice for today is: be flexible. No one set of advice fits everyone and every day. For instance, while cheese and beef are relatively cheap where I live, I know people in other parts of the country who pay twice as much. And the food that's cheap today may not be next week, and vice versa. Corn meal and chicken wings used to be incredibly cheap. Now, corn meal here is often around $.75 a pound, while I frequently get white flour for about $.25 a pound and chicken wings sometimes cost close to the price of chicken breasts. A couple of weeks ago, I found whole wheat macaroni on sale for less than the regular.
Soup is a fascinating and versatile dish. It can be the cheapest of meals or incredibly expensive. And as the old story about stone soup should show, you can put almost anything into it. One caution up front: be sure of your food safety and handling. Don't cook the soup at too low a temperature, for example, especially if it involves meat. If you don't know these things already, try here for advice: http://www.foodsafety.gov/
I'll leave the gourmet soups to the foodies and address soup for tightwads. Soup is easy and cheap to make and doesn't really require a recipe, just some common sense and a willingness to experiment. I buy beef and chicken soup base in a jar that you scoop out one teaspoon per cup of liquid. One jar at $2.99 makes 91 cups of broth, which is about $.10 for 3 cups of broth. Those who are just trying to cut corners a little can pay a bit more for a better quality of the same product and still get it for less than $.25 for a quart of broth. But for those who badly need to pinch every penny, make your own which is much easier than people realize. Save bones (separated by poultry or beef) in the freezer until you have a couple of pounds worth. Put them in a pot and cover with water at least an inch or two above the top of the bones and add about a tablespoon of salt. I recommend adding a tablespoon or two of either lemon juice or vinegar to extract extra calcium from the bone, but I like the flavor. You can save vegetable peels the same way in the freezer and add them to the pot as well. Bring to a boil, then lower to a simmer, cover and cook for a couple of hours, then strain out the bones and peels. Check the water level in the pot regularly and add more if it looks like the bones will poke out of the water. This is best in a slow cooker, cooked over an entire day. I don't recommend using bones that have been in contact with people's mouths, but some older books point out that boiling is supposed to kill germs. For vegetarians, by the way, you can get or make the same kind of stock with vegetables.
So, now you have stock. What to put in the soup? I'm a fan of meals with a good amount of protein, so I like some meat or at least some legumes in it. I make soup with leftover cooked meat, but if you are using raw meat, brown it at least a little before adding to the pot. Proportion to the amount of stock, up to a cup of diced meat per quart of liquid. Unless you're more interested in cutting calories than expense, you'll probably want to add a starch-potatoes, beans, lentils, split peas, rice, or pasta. Keep in mind how much water each will absorb in cooking. If a pasta recommends 3 cups of liquid per cup of pasta. don't add 2 cups of pasta to a quart of broth. Instead, since you want this to have some broth left, cut the amount of the dry product by about 2/3, and for 3 cups of liquid, only add about 1/2 to 2/3 of a cup of pasta. This is part of that common sense I mentioned. If you're using leftover cooked meat, you can put in the meat and the starch at the same time, cooking until the starch is done. If you're using raw meat that's been browned, cook until the meat is completely cooked through before adding your starch. If you want to add vegetables, add them with enough time to cook before the starch is cooked. This is a preference thing. Some people like their vegetables to be mush, some want them almost crunchy still. And seasonings. Pick appropriate ones for what you're cooking and add them early enough to give the soup flavor. I find a tiny touch of cayenne does wonders to spice up a bland bean-heavy soup
The first time you try making soup like this, keep it simple. Use a single precooked meat, add a starch you have experience cooking, and only add one or two vegetables and simple seasonings-2 quarts of broth, a cup or so of diced cooked chicken, a cup or two of diced potatoes, a few diced carrots, simmered for 20 to 30 minutes with some salt, pepper, and garlic.
For those who are desperate, I think soup is the food of hope. Beans, split peas, lentils, and brown rice are regularly less than $.70 a pound in my grocery store. I can make a pot of bean soup that, with some bread, feeds 4. About $.10 for the stock, about $.25 worth of beans, about $.05 worth of seasoning, and some day-old white bread about $.35, at a total of around $.75 for the entire meal. If you mix a legume (beans or split peas or lentils) with rice, you also have a complete protein. Potato soup, made with a little milk, is filling and a good protein. And look for bargains to add vegetables. We live a few blocks from a produce market that has a back corner where older produce is put out at $1.00 a small basket. I can get several pounds of tomatoes or eggplant for a dollar, but we don't use produce quickly enough to take advantage of that. That's important to consider: will you use it before it turns?