On the Southern Gardening forum there is a thread addressing your question. I'm interested also in a fast growing evergreen tree. I'm considering some type of bamboo.

Elderberry or Bamboo... or both.

Mimosa trees or Empress trees would be at the VERY BOTTOM of my list. Both are a tier 1 invasive (extremely harmful to the environment). Both are weak wooded and short lived. Both are deciduous.

Thuja 'Giant Green' is one of the best rapidly growing evergreen screens. They grow about as fast as a tree can grow. They are evergreen. They are virtually pest, disease, and problem free.

The downfalls of a solid Thuja 'Giant Green' screen are that they are boring if planted in a monoculture, they are starting to become overplanted as more and more people hear about them, and they can grow too large for some areas. If you do plant them, I would recommend a mixed planting of them and other types of trees for variety. I would also stagger them if possible. That will produce the fasted visual closure rate and provide at least some protection if one is lost. Otherwise, you could end up with a giant ungreen gap one day. Always pick single leader evergreens to reduce likelihood of damage by snow and ice load (Green Giants usually hold up very well with snow and ice load), and take mature size (and maybe even ultimate size) into consideration.

Here's a link to a picture of them. There's a neat little feature on this page ... if you roll over the picture it shows you a yard without the trees, then "roll off" the picture and see the same yard with the trees.

Here is a link that might be useful: Thuja Giant