Soup is pretty budget-friendly as is because most soups are primarily water! But there are a few other things to consider that can save a lot of money on your grocery bill while still making a delicious meal.
First and foremost, when you are deciding which soup to cook you should consider what resources are most cheaply available to you. Are there leftovers or forgotten ingredients hidden in your produce drawer, tucked away in the freezer, or stashed in a cabinet? Take a thorough inventory of your kitchen and try to come up with a recipe that uses most or all of what you already have. There are online tools that can help you come up with recipes based off of ingredients you already have, like MyFridgeFood or SuperCook. Another approach would be to consider what cuisines or what flavors meld well with what you already have–leftover Indian carryout can make a delicious and filling soup with little more to purchase additionally than onion, celery, and broth.
Secondly, focus on using less expensive but still flavorful and nutritious ingredients. This may mean shopping for ingredients that are in season or that are on sale. In-season ingredients will make the best tasting food because they are fresher and the most ripe. But ingredients on sale are not necessarily bad options for flavor, stores may simply be trying to clear inventory to bring in new products. Using certain cooking techniques can bring a lot of flavor to even the simplest of ingredients. Roasting root vegetables like parsnips, turnips, and onions is a good way to bring out as much flavor as possible and the flavor carries over into the soup as well (nearly every vegetable tastes even better when roasted, so go crazy!).
Finally, consider cooking without meat or using cheaper cuts of meat. Soupa avgolemono is a Greek soup made with lemon, eggs, and rice or orzo–you can add chicken for more flavor and substance, but it is completely delicious and filling with just inexpensive ingredients! If you want to use meat, whether for flavor or nutrition or both, look for fattier cuts or bone-in pieces. These will be much cheaper than boneless skinless chicken breast, for example, and will also have so much more flavor (a key tip for any cooking: fat equals flavor, do not be scared of it!). With a little change in technique, you can use inexpensive meat to get incredible flavor. Homemade bone broth is also an inexpensive way to get the rich flavor of meat without the price tag–stay tuned to learn more about making bone broth cheaply!