RE: Which trees??
Leyland's tend to be very popular in our neck of the woods for exactly what you're talking about, but we're zone 7 and you all are zone 6 (southern/eastern part of state) or zone 5 (northern/western part of state). I can't say I know where you're located in NY, but I do know that Leyland's are good for hardiness zones 6 -10. You may already know if they do alright in your area, if not, ask a local nursery. They are very inexpensive (about $24 for a three footer), and very fast growers. Watch out for bagworms!!!!!! They will kill a group of trees and you will have a goofy looking hole with replacement trees trying their best to catch up.I believea product like "Seven," whichyou can buy at Lowe's will take care ofthem should they appear.
There are also various cultivars of Arborvitae that can be looked into. I feel like I'm getting a little longwinded though, so let me know if you'd like any help - and I'll give it a whirl.
P.S. I can probably scrounge up some bulk growers that I can hook you up with that are affiliated with a grower I use - I just have to go through a filing cabinet if you're interested. The $24/tree price I told you was a number I remembered seeing in a local paper in the classified section, so they're not hard to come by.