I garden on a much smaller scale, and I don't use anything except mulchy stuff that I find around the place, a lot if it is just weeds I pull or chop down in the garden itself and the spent vegetable plants, also leaves raked up from the yard each fall. A lot of time, I just let low growing ground cover weeds like purslane or creeping Charlie do their thing, especially under tall plants like corn or okra.
I might be more sensitive that others, but I think plastic has an unpleasant chemical smell, especially if it's left out in the sun so I don't like it. I do use some plastic pots but that's because I haven't found a better option, yet. I collect them for free and after sitting out for a long while I figure most of the outgassing is done, or at least that's what I tell myself.
I think cardboard is pretty gross too. I did a short stint receiving product, mostly from China into a big distribution warehouse. My oversensitivity may be in play again but the smell when one of those trucks was opened was unpleasant, at best. Even if the production of cardboard and inks used isn't an issue, which I don't believe, whatever might have been used to protect against infestations certainly is.
I let big-rooted weeds like dandelions, thistles and dock along with things like radishes and turnips do most of my tilling. If more is necessary, I use a shovel or hoe. I don't like the roar and stink of gasoline powered machines and enjoy my gardening lots more since abandoning them. Getting rid of that big tiller was the best thing I ever did as far as making things easier.