Before anybody can make suggestions, we need to know what the conditions of the site are. Is it sunny or shady? What is the type of soil? Clay or Loam? Is it acidic or alkaline? Does it get sufficient moisture?

First, you need to decide 1) how fast you want your privacy screen to grow, 2) whether you want vines, shrubs, or trees, 3) if you want evergreens for year-round privacy, 4) how much sun/shade your plants will live in, and 5) how much work you need to do later to keep your living privacy screen.

If you want vines: grapevines, a non-invasive honeysuckle variety, ivies (evergreen), or clematis (will not provide much privacy but very beautiful in bloom) would be nice.

If you want a hedge: look at holly varieties, euonymous, privet, and lilacs. Some of these are evergreen or will keep their leaves during the winter in your zone.

If you want other shrubs or bushes: climbing roses, Rose of Sharon, Snowball bushes, junipers, and photinia. Photinia will keep leaves during the winter and junipers are evergreen.

There are a number of trees, like poplars and junipers (evergreen) that can add privacy if mixed with shrubs and bushes.

If you want something in the next few years, grapevines would be the fastest to add privacy with the fewest plants. Hollies and privet make good hedges and would be the easiest to care for but would take more plants and take longer to grow for privacy.

Some of the plants I have suggested are not invasive in my area but may be in yours. Trumpet vines and virgina creeper are very invasive here, even breaking fences in just a few years. Grapevines, if not provided with support and left untended, will do the same. English ivy may be invasive in your area, but here it only grows in the shade. Privet can get rather tall for privacy, it will spread from the roots without being invasive, but needs to be trimmed and kept in check with a spade.

Also, some plants are more pleasing to the eye than others, and you might even decide on a variety of vegetation. If you mixed grapevines with other plants, you could take out or hard prune the grapevines when they become too ungainly.

My personal choice for privacy would be a holly even though it might not grow as fast as some others: it doesn't take much care, it can be pruned easily as a privacy hedge, it is not invasive (at least in my area), and it will stay beautiful all year. Ease of care, quick growth, and final size will depend on the variety.

Other gardenwebbers will give you more info. There are lots of other choices out there. Best wishes.

Blueheron, the site is very sunny,the soil mostly clay and acidic and it gets sufficient moisture. Thank you for answering my post. Vique.
ElGrillo, whew, you have given me a lot to think about. I will go over all your choices and post again later. Thanks for answering my post. Vique.