Potatoes grow in small spaces and don't require a lot of attention, but they won't save you much money.

I think the most bang for your buck home garden are things you wouldn't buy because they are too expensive but can grow easily. Herbs are a good choice.

In my garden I mix those with things that are cheap, but fun:

• asparagus (perennial, almost zero effort, get a few delicious means out of the 5 plants we have each year)
• fresh beans (easy to grow if they don't get eaten by various garden mammals) and not something I usually buy fresh.
• dried beans (not a good use of a small space because the yield is low compared to fresh beans but super fun)
• potatoes (fun, use last year's as seed and augment)
• sweet potatoes (fun, still producing them from slips I bought in 2022.)
• tomatoes (local fresh tomatoes are outside of my budget in general except for the ones I buy for canning in September)
• garlic (very, very low effort and I use last year's as seed)
• carrots (fun and delicious)
• raspberries (I never buy fresh berries, and the raspberries need nothing more than pruning in the spring)
• weed (almost free weed rules)

I don't grow lettuce or most leafy greens because I have a slug problem (no advice please) but have hydro lettuce on my "want to try list".