I'm probably not the best person to contribute to this thread as gardening is my hobby and I admit to spending quite a bit on that. I also live in a temperate rain forest, so can't help with the irrigation comment either - it would be interesting to get hints from a frugal gardener in an arid climate...I'm thinking wicking beds perhaps, I'm pretty sure Paul would promote hugelkulture!
I collected my tools over a number of years, some bought myself, some as presents. I think you can do a lot with a good fork, a trowel, and maybe a spade to start off with. Old tools are often better than any you can buy new, unless you do spend a bit. I'm not sure if we have a thread on a beginner tool set and how to obtain it....
I'm in the process of building up my landraces, but hope to spend less on seed this year. Other than that I don't think I spend anything on my annual veg patch....(but far too much on my experimental plantings and my polytunnel this year

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