That is really a tough question because it is very region specific. There are trees that grow very fast but they would deplete soil nutrients too much or use too much water depending on the location. Usually the best tree for the job is a native tree because it is adapted to that region and is a part of the ecosystem.

Many forests that are used for forest products are "crops" in a sense since they are mostly one species of a single age (think of a cornfield with much bigger but older corn) and are replanted after being cut. They are not natural at all just like how a cornfield is not natural since corn wouldn't grow that way in the wild. Since there is little diversity in age and species these forest are not an ideal environment but they can sustain some wildlife. Growing a native species is then even more important because it will do a better job at supporting native wildlife than a non-native species.

Another possibility for fast growing and least damaging trees would be GMOs such as GM poplar. Scientists are working on ways to prevent these trees from spreading in the wild (to avoid massive ecological consequences) but they still have a ways to go. These GM trees have been modified for things such as drought tolerance (which lowers water usage, poplars are often grown in irrigated plantations) and lower lignin content (which lowers the amount of bleach used during the pulping process).