What trees to plant?

Jester7891

Hi, I live on the NJ/Pa border, USA (zone 6a) wooded area. For tax purposes I had to clean up a forest that had been long neglected. I tore out lots of vines and brier bushes, cut down dead trees and pruned others etc. The forest looks much better now but there are lots of open spots. The forest is on a hill so now when it rains, I get a lot of run off and pooling of water. Most of the trees are popular about 30-40 years old about 50-70 feet up (I'm guessing). I want to start to plant trees in the spaces in between. Deer is a big problem but I can put simple fences around new trees for the first few years. What trees do you suggest? They will need to be able to grow in shade (from the trees above). I am also interested in any other ground cover that will help hold the soil in place and slow the re-growth of the vines. Thanks for your input.