Are you willing to prune annually to keep plants to the size you choose, either height or width? When you say you want height, are you thinking high enough so that someone can't see over it, or so that the 8 story apartment across the street can't see into the yard?

It sounds like the area where the hedge will be is in full sun, not shaded at all. This is an advantage since it means you are more likely to have leaves densely clothing the hedge top to bottom. How is wind exposure?

Think about whether you want all of one kind of plant, which looks more formal, but will be a problem if a pest or disease infests your hedge or even if a plant dies, trying to match the older plants; or if you want to have a mixed species hedge, using repetition of groups of plants. It looks less formal, but will be more resilient in the face of problems and may offer more variety in the way of food and habitat for birds.

IME if you have a good quality foundation, the roots from a hedge won't be a problem.

I am right on the edge of 5a/4b, and IME, if you want bamboo, you will want to be OK with one that might get killed back in particularly harsh winters, like the last one, though mine hasn't died back most years. Mine (one of the hardiest Fargesia, it gets only to about 6' here ) also doesn't do particularly well with staying upright with heavy wet snow, so you may lose some privacy in the winter. Others from farther south or with different varieties may have different experiences, but that is my experience a bit north of Concord, NH.

Arborvitae is fine if you don't have deer. Depending on the species and cultivar you choose, they can range from 8' or 10' to 40' and have a color range that includes yellows, greens, and some lightly frosted or variegated. Some types are more likely to grow multiple stems, and those are more likely to split apart in heavy snow or ice, so if that is an issue for your yard, you may want to choose carefully.

There are also some narrow hollies and junipers. Skyrocket juniper is a form of J. scopulorum which is from the western US, so is more prone to disease in humid areas. Sky Pencil holly is a form of Ilex crenata and looks a bit like a narrow boxwood - the leaves aren't prickly. There are narrow yews such as Hicks yews, but yews are particularly beloved by deer, so if you have deer, you don't want yews. I don't have any experience with the narrow forms of any of these plants, so perhaps others can add info about how they fare in the landscape.

There are also some fastigate small to mid-sized trees such as Japanese and other maples (Acer), Sweet gum (Liquidambar), Hornbeam (Carpinus) as well as a number of fastigate/columnar evergreens such as varieties of pine, fir, and spruce. Many of the evergreens will grow to tree height, though not all. In general these will tend to be more expensive since most require grafting to achieve the narrow form.

Thanks for all the advice. As for height I'd say at least 10 feet. Deer aren't a concern here and wind shouldn't be either but heavy drifting snow can be due to the location on a hill side. Foundation is cinder block and fieldstone and leaks a bit in heavy rain.

I have arborvitae "Emerald Green". I was never a huge fan of arborvitae, but this particular hybrid is really nice. If, as you say, deer aren't a problem, then it may be a candidate for your screen. It is really a beautiful deep green (evergreen of course) and grows well, but not rampant. It also stays quite tight at about two to three feet wide, maximum. Mine form a very nice and effective screen.