Hi Craig, I don't know where you are located, but there are great ways to learn more about the biodiversity of your area. One thing we have done is to join a local Wild Ones group which focuses on which native plants belong in your area. In some cases, what you have there now, is not what was historically there. I've also looked at historical state maps from back in the 1800's when they did surveys of the land (mostly looking for ways to exploit it!).
We also have woods behind our house that have been disturbed quite a bit. There is a large oak and some hackberry trees that are legit, but there is a ton of honeysuckle that we want to get rid of since it doesn't belong. There is a Norway Maple and Box Elder. We'd like to take down both of those. We have a lot of black raspberry brambles and then a lot of invasive junk. I believe there must be earthworms present in the soil since there is no duff and the leaf cover is gone by early to mid summer drying out the soil badly. I may work to try to change the soil if I can. Maybe I can chase the earthworms into my yard and out of the forest to make a healthier forest.
For me, I plan to only put native plants, shrubs and trees behind our fence in the woods. This will include food for the birds and maybe some food for us too. In my yard I will have native plants, but also a huge variety of food plants. I'm planning on growing mushrooms, but I'll probably do it in the yard, unless it's something like chicken of the woods or others that I've seen in the area. In the beginning I wanted only native plants, but then I read something very convincing about how we can do more good by growing our own food than going with exclusively native plants. Now, I"m trying to strike a balance between the two. I believe many of the native plants will be good companion plants for my food. They will support local, native pollinators and they will be beautiful.
Another thing to consider before changing your woods is to try to find out if you have any sensitive areas nearby. Sometimes there are endangered or threatened plants in those areas. Purists will say that the genetic stock of those plants should not be mixed with genetics from other areas. Plants that may exist across a large span of land (across many states), may still have particular genetics for specific sites and will do better there than if you move them to a slightly different climate.
Good luck with whatever you decide to do!