I'm going to go against the grain of most comments here and say bamboo is your best choice.
If you or your neighbor has livestock, no worries, they'll eat it. After all, bamboo is the largest member of the Graminae (grass) family. The protein content of bamboo runs between 20 and 30% - higher than alfalfa - which means cattle like it because its a grass and goats like it due to its high protein content. In short, there are few plants that grow faster and provide a higher quality forage than bamboo. No need to do a lot of work to control it - make the livestock do that for you. Plus it's the best option for screening out neighbors. And it makes a highly sustainable building material - http://erdakroft.com/Erdakroftfarm/quincha.html
If your not running livestock on your 40 acres you might want to consider doing so. You can run them along the fence line to keep the bamboo controlled so it doesn't cross into the neighbors property. Can't recommend trenches with barriers, they'll only last a few years - the rhizomes will eventually find a way over, under or through them. Besides they are costly and labor intensive to install and maintain. Two small bamboo leptomorph (running) bamboo plants would be sufficient to cover the view in a few years. I recommend any of the members of the genus Phyllostachys in the 30' to 40' tall range. They make better forage and have a higher protein content than the taller species. You could also plant pahcymorph (clumping) species but most of them aren't nearly as cold hardy as the Phyllostachys. One of the most cold hardy pachymorph species is Bambusa multiplex, of which there are several forms. For hardiness and stout, versatile culms, go with the standard form. With much shorter rhizomes they'll only spread a fraction of the distance of the Phylllstachys so you'll need a lot more plants - http://bamboo.org/index.php