I have a feeling that the answer to this might be anything that you can grow from seeds. So, fresh fruits, vegetables, beans, grains, etc. then, like tomatoes or snow peas or apples or wheatberries. The thing is that these all take time to transform from seed to fruit, so if you include time in your constraint space these don't work. But you didn't so here you go :D
As someone attempting to grow from seed here in Central Texas:
It would be SO MUCH cheaper for me to buy store bought.
You have to factor in a watering costs, soil quality, fertilizer costs, and time commitment. Oh and potentially overhauling large swaths of your yard to grow crops and flowers to encourage enough pollinators to show up.
I spent probably over $1,500 this year getting my yard in suitable enough shape to grow, after a complete bust on any kind of yield last year. I also grow herbs indoors, and yes that can be more cost effective. That isn't to say it's not worth it, I'm about to have an insane yield of tomatoes that I won't know what to do with. I currently get to make my own fresh bruschetta every week with home grown basil and tomatoes. I get fresh strawberries off the vine every day, though the bushels aren't very large. If all goes according to plan, I'll also have some bell peppers and okra later in the season. All grown from seed. I have morning glory and passion flower vines that have volunteered all over parts of the yard, the latter being a critical food source for butterflies, so I now have a few dozen butterflies flapping around on a given day. I also have a ton of volunteer sunflowers after setting up bird feeders with black oil sunflower seeds as feed.
It's wonderful, my yard is slowly rewilding and I love being able to grow a little food. It'll get cheaper over the next few years to maintain. But it certainly was not cheap to get here! Container gardening is cheaper, but you still have to have the right light sources and watering schedule. If you live somewhere naturally rainy and sunny in equal measure, and the climate isn't trying to kill you, then it might be cost effective. It was at one point in time. But it isn't here, now. Still worth it for me though.
Yeah only cheap if you don't include your time. And the cost of land. But as a Florida food gardener - OKRA is like nothing else. It grows even in the summer here, is beautiful, the flowers are lovely and my whole family loves it. If you grow it, you can pick them when younger, and the few you inevitably miss, save for seeds. Nutritious and delicious, and in hot climates, cheap.
Beans are the obvious answer to the OP's puzzle though. Beans and rice, build up your spice cabinet, endless variety and so delicious, cheap, and healthy.
I tell ya, I tried okra last year and it was a total bust. Had enough seeds to try again this year, started them indoors. Of the 10 seedlings I sprouted, six made it into the ground in March, and only two are still growing. They're by far my slowest growers, but the good news is they look like they're finally picking up speed and are looking strong. They're about 18"-2' tall now. I hope they survive the next 3 months set to have more 100*+ days than not.
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