Wow! There must be a lot of tree-cutting restrictions back east. Out here in the west, it's clear-cut all the way.
If you can remove some trees on the south side of the house, you will also get some solar gain in winter for your home. I would go crazy if my house was buried in trees. Another type of claustrophobia, I guess. It might also be a viable argument for cutting the trees.
If you do have valuable trees, DO NOT attempt to mill them yourself. Trees of that type have more value as veneer wood, not lumber. Find a couple of people who deal in veneer wood and get them into a bidding war.
If you do have some trees cut down, find a local farmer with a large tractor and have him pull the stumps, as they won't rot fast enough for your purposes, no matter what you do.
Chemical gardening could well affect groundwater, but organic could be different.
Have your soil tested by a reliable ag lab. I would recommend Kinsey Agricultural Services. Kinsey literally wrote the book on agronomy: "Hands-On Agronomy" (2006, Acres U.S.A.). He also has an hour-long video with the same title, but of course it isn't as in-depth as the book.
http://kinseyag.com/I don't have any connection with him other than to soon be a customer of his lab services.
Sue