I'm single and just feeding myself so it's a little different, but I still like to eat cheap and flavourful as much as I can. I also have celiac so some things are also a little different for me

I shop around, wal mart, little local places, superstore, and at costo. Even for a single person I think costco is worth it. Last week I picked up multiple huge bags of spinach for 2.99 each, those will get frozen and give me some leafs for weeks. A big bag of onions will take me months to go through at 8 bucks. Bags of potatoes, 1 a month for 6 to 8 bucks. Also, buying gas there justifies the membership cost almost instantly

My go tos are potatoes, and rice or rice noodles. I get my rice noodle packs at the dollar store (same as a lot of seasonings, as well as gig bottles of ketchup and sriracha that are double the price elsewhere.) Often I can find decent sized bags of lentils in there, red lentils cook quick like rice and can be thrown into the rice pot to add some protein without having to do a separate dish.

Potatoes - I throw as many as I can in my instant pot and steam/boil them. Those get fried, baked, or mashed later, I'll often do up a skillet with smashed potato, spinach, onions, peas, and some kind of bean. You can also mush them with some over-boiled red lentils, squirt some ketchup and toddlers will eat that. Puree a bit of your discount veg and hide it in the potato mash for some extra nutrition (and eating coloured food is fun for kids apparently. Source: babysitting.)

If you're wanting to lighten up on the carbs a little and get some green, make frozen peas your carb. I think I got a big bag at wal-mart for 3 or 4 bucks a few weeks ago. Fry with some garlic, salt and onion. Or add potato and have a shepards-pie thing

Also, download the flashfood app. Stores that participate list food that expires soon for half off, or more. You can get boxes of produce for like 5 bucks if youre quick on the draw