None of those are particularly "fast" examples.
Radish is fast - 3 weeks to harvest for the small types. I don't like it much, but it's fast. You'd need to let some go to seed for seeds.
Since your "not actually very fast" examples seem to mostly be things that are usually propagated by clone, potatoes, sweet potatoes/yams, shallots, sunchokes, horseradish. The latter two can approach being weeds, so choose a spot carefully.
Not having to buy seed would suggest perennials - if you are south enough, olives; chestnuts, almonds, peaches, pears, apricots, mulberries, apples if not too far south, grapes, currants, raspberries, strawberries, asparagus, kiwifruit, rhubarb, blueberries...
Any open pollinated variety can serve as its own seed source - given how slow most of your examples are, that leaves pretty much all vegetables and grains open to include.
If you can manage to be somewhat polite and sociable MANY things can be had for free (or a little labor) by contacting a gardener who is already growing them, and getting some prunings/slips/divisions or excess seeds. Be prepared to do the same in return, when the time comes.