It would be better to cover with flattened corrugated cardboard first. This helps to smother anything that is growing there, including grass and weeds. For the keyhole garden areas, start by using gardening fork to make holes and fracture the ground -- I stand on it, step off, and then tilt (not dig or lift up) -- then put down a layer of compost or composted manure and any other amendments you need for your soil (like lime). Material you Put down in this layer under the cardboar can be weedy or suspected of containing weeds seeds. Water well, then cover with the cardboard and soak the cardboard. Build your keyhole gardens on top of that.
For the wood chip area, with the cardboard down, you only need enough to hide the cardboard initially, but the cardboard will break down eventually so you will need more and this can be added later or you can put down several inches from the start. If it's going to be a very large area and not just paths, you may want to lime the area first if you have acid soil since the wood chips and subsequent fungal colonization will contribute to acidifying the soil.
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