One big problem with netting is that grass, weeds, and such grow up into it and short it out. Weed whackers are murder on the netting. I would not recommend netting in a woodlands setting. It’s more of an open field thing. And you need to move it often or find a way to manage the grass or...
I’m envisioning an area maybe 80’ x 100’. Pure woodland. Maybe not real level?
You will need a fence to contain your chickens. In an area that big you would probably be able to do that with a 4’ high fence but 5’ high is better. Unless you have weird chickens yours can probably fly that...