Some things are going to depend on your climate, so what has worked for me may not be a good fit for you.

That said, things I’ve had success with as a lazy gardener in a cool temperate climate:

• beans: pick every few days and eat fresh; keeps producing through the season
• lettuce: choose a variety from which you can pick a few leaves at a time rather than harvesting the whole head
• silverbeet/chard and spinach: pick leaves as needed
• Jerusalem artichokes: takes all season to grow, but produces an abundance of tubers; use them like potatoes
• leeks and spring onions: use the green part, leave the roots in the ground and it will regrow
• radishes: quick to grow, can be eaten fresh or cooked
• beets: can pick occasional leaves to eat while the roots are growing
• perennial herbs (rosemary, thyme, oregano, chives)
• parsley
• Asian greens (pak choy, choy sum, tatsoi, etc)

Mostly those things have grown with little attention from me apart from water when it’s dry. Many of them can be grown easily from seed, which is cheaper than seedlings but takes longer.

Let a plant go to seed and you get more for free. Leeks, spring onions, radishes, leafy greens, parsley are very easy to do this with. Save a few Jerusalem artichoke tubers for next season’s crop. Let a couple of bean pods dry on the plant, save the beans and plant them next season.

If there is a community garden near you, that’s a great place to ask for advice about what grows well in your area. They may also be able to help you get started with seeds or cuttings.