Some stuff you might need to know:
1) A woodchuck doesn't exist (yet?)
2) Piggies around wood trees might not survive, so keep one tree non-wood. Unless you're taking care of the pigs.
3) There are people who kill wood trees everywhere, your block, you name it.
4) The max harvest from a wood tree is about 80 planks they sell for 4 currants each, so that 320 currants a tree with the max Gardening skill. The tree might need to be in its best shape (with the help or fertilidust [sometimes lite]) to get you 80 planks, otherwise you'll end up with 40 or 60 planks which also isn't so bad.
5) It takes 6 Pets and or Waters to get a stem or arm of a wood tree back, one fertilidust sprinkle does the trick.
6) They are rare, when on the last segment, they can be cleared, if you can, please try to pet,water, fertlildust it to keep it alive.
7) There are achievements (some difficult) related to the tree.
8) There's a group that protects the wood trees on a street, feeds the piggies, and doesn't mind anyone being there with intentions to harvest. By popular group vote, it is only going to stay 4 wood trees.
From experience, there's also another way to benefit from the tree. You can donate to a shrine, one plank at a time, get a ticket, maybe a Musicblock... and sell that. The incredible harvests should help. This claim has not been confirmed yet... but the credit goes to MM.
Thanks for reading!