I have poor clay soil, look into the Ruth Stout gardening method, helped me tremendously.
No till growers on you tube puts a lot of good information on small scale market farming. Elaine Ingham, probably spelled wrong, soil food web, Jole Salitin, Charles Dowding, Paul Guachi back to eden. Stefan Sobkowiak, I had to look it up but that one is spelled correctly.
Weeds are a disturbance mitigator. Weeds come after disturbance and beging to restructure and recover the soil. Tillage burns up organic matter and kills or makes soil inhospitable to creatures that build soil. Weeds are trying to fix the disturbance but we generally fight them as they try to perform their processes. Then we wonder why our soil stays the same year after year.
With heavey clay soils I would start with a one till. Two really but done at the time. I woukd till straps on the sides of the beds then move that tilled soil on the garden bed. Then I would cover with compost and till that into the bed. Then I would plant something into it with a big powerfull root system like one of the giant sunflower varieties. I would either use 10+ diffrent cover crop seeds or just kind of let the weeds grow in it with whatever I was growing. Then I woukd put something in it to over winter. Like winter rye grass grain. Not rye grass like in your yard.
When working in a no till system some of your best friends could be the annual weeds that grow in your area. Same goes if you can't buy fertilizer. Weeds are easy to grow with nothing and make lots of green matter for compost for row cops. The compost you make can go farther if you make compost tea. Even if you just soak it in water and stir it occasionally.
Plant fruit trees, brambles, and vines. It's a lot more work to try to feed yourself on annuals only.
Forget tomatoes as a food source. Tomatoes are a sauce. You are going to be sick sick sick if you only have 200lbs of tomatoes to eat for the winter.
Sweat potatoes. Those fucking things. I have some two year old ones in a box in the garage. I used them to start slips this year. Perfectly edible, perfectly viable after two years of no special storage. If you are warm all year. Don't put them in your garden or you will never get rid of them. I would think you would be silly not to have a patch some where though. You can eat the foliage also on sweat potatoes.
Lambs quarter is an edible weed that grows big and strong in about any decent garden soil. Its leaves taste like spinach and stems kind of like broccoli if you cut it small. After it gets larger the stems get woody but the leaves are still good. I eat them raw and cook them. It's one of my friend weeds and one of friends weeds. I have a buddy who jars up a bunch of it every year. He went and found one and dug up it and transplanted it at his house so it could seed. Now he has his own supply that basically grows its self.
Find stuff that grows like a weed in your area.