We have a beautiful woods, but many of the trees are diseased or infested with bugs. What can we do to help restore the health and beauty of these woods?

We are seriously considering using goats to help clear the noxious invasives from the understory, and thin some of the natives (there are only so many blackberries we can take). Some of the trees will be cut for firewood, and we would like to know which and how many should be harvested to increase the health of the rest of the woods.
Many of the ravines, caused by rain, are in the process of being "filled" with down trees to help stop erosion. Is this a good practice, or is there something else we should consider to help lessen erosion issues?
This property is considered "Greenbelt".

I have heard of goats being used before, but haven't seen it myself. It's an interesting concept. 

As for using downed woody debris to control erosion, it's not a totally bad idea. That's very similar to how we control erosion on trails, by using waterbars to divert and slow the flow of water where there's no vegetation (like on a trail). http://www2.dnr.cornell.edu/ext/bmp/contents/postharvest/post_waterbar.htm
The best idea to control erosion on slopes is to make sure its well vegetated. Plant native shrubs or trees. They'll use that water, as well as holding the soil in place.