I'd carefully scout potential routes and pick one tht requires the least disturbance. I would avoid moving any dirt, and cut as few bushes and saplings as possible. If you leave behind walking trails, that may be considered a benefit to the neighbor, but leaving behind muddy scars, piles of cut brush, etc. would be a poor way to repay the neighbor for letting you cut firewood. Even if the neighbor says he doesn't mind you making trails, I wouldn't assume that means you should tear up the ground. For the most part, if you don't scrape up the soil too much, cutting shrubs and small trees has little impact on the forest. and in a few years you won't be able to tell where the trails were, unless you keep using them.