Hello Middle Aged Beginner, I think you need to decide if you are going organic all in one jump or if you are doing it bit by bit. You're talking about putting carpet over part of the ground. Very controversial subject.Maybe you could Google on that subject and make up your own mind. Personally I would use weedkiller before I would use carpet, but check it out and decide for yourself.
You have a patch of Brambles ? Some people seem to find them a problem but I think there are much worse weeds. For Brambles I find if you chop them at ground level (not nice job getting rid of the choppings, but they do burn well) then chop at ground level anything that regrows, if anything has the cheek to reappear after that you can chop or give a liitle squirt of weedkiller. I've cleared great big bramble parches by that method. Good luck with the project.

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