some screens that are good in VA zone 8A:

Chindo Viburnum, Illicium anisatum, Elaeagnus fruitlandii, Osmanthus fragrans, River Birch, Magnolia virginiana australis, Bald Cypress, Yaupon Holly, Magnolia grandiflora, Live Oak, Carolina Laurel, Persea borbonia, Deodora Cedar, Yoshino Cryptomeria, Lusterleaf Holly....

i dont do your zone .... so i will leave specific suggestions to others ...

first.. i would not recommend anything advertised as fast growing... fast to grow... fast to problems.. usually structural ... at least... you are not planting near a house in a small yard ... i have oaks growing 3 to 5 feet per year in my MI ...... once they get going.. i dont know why you need anything faster than that ...

second.. start thinking in tree time .... i know you want it done last year ... but if you start thinking in accomplishing this in 3 to 5 years ... and forward .... you will make better decisions ...

third ... NEVER PLANT A MONOCULTURE .. one problems rolls around and your whole planting is at risk .... and it usually happens the year after you are finally happy with the result ...

4th ... if you limit your project out at the property line.. you will be waiting a lot longer than if you can plant some larger trees in the lawn between the house and the property line ... one well placed tree between the most looked out window ... and the new house.. will block that house from that window a decade faster than 50 trees out at the property line ... sooooo... dont limit the plan to such ... have a wider approach to it all ...

lastly.. you dont talk about size ... but too many peeps think bigger is a better way to start.. but due to the increased stresses ... often.. small trees get established faster .. and out grow larger transplants ... so its a false economic narrative ...

if this is DIY .... good primer below.. if you need such ... proper watering might be the biggest challenge .. for the first 2 or 3 years .... i single drip irrigation line.. that is hose based ... can be a cheap and very useful investment .... lawn watering is seldom proper ...

good luck.. nice dog ...

btw.... where is the property line between the playscape and the tree line.. how many feet????

ken

https://sites.google.com/site/tnarboretum/Home/planting-a-tree-or-shrub

Arborvitaes are very long lived, Leyland being a conifer shouldn't be inherently short-lived either. Where premature failures develop with the latter is cultural issues such as bound roots causing them to blow over after the tops get heavy enough. Or disease problems in unsuitable climates.

Since you're 8a, I assume you're coastal (tidewater area). No matter what variety you're looking at, look at the root structure and height. Virginia isn't hit by many tropical storms, but the coast does catch it's share of brushes. And hurricane gusts (as well as straight line winds of squall lines) will lay down the most common screening trees/shrubs especially as they get taller. If the soil gets and retains wetness/soggy in any heavy rain at any point, then any tree there is likely to be compromised.

Thunja green giant...tall and fast

growing

One piece of missing information is the width you are willing to take up with plant matter. Another is the height you want. For instance, Thuja Green Giant, one posted recommendation, can grow to 40’ tall and 20’ wide. The photos don’t suggest that you have that kind of space to use, and keeping plants that want to be so large to a reasonable size is a lot of work. Likewise, the Austrees can develop quite a bit of width and height. Until you know if the next door house is likely to be 1 or 2 story and how close to the lot line of is likely to be, it can be tough to decide on the best screening size. Also, any part of the plant that grows over the property line is fair game for the neighbor to prune/remove in every jurisdiction where I have lived, so you want to plant where most of the plant grows on your side of the property line.

A few more questions:

-How much pruning are you willing to do on a row of plants that is so long? Fast growing plants will either need considerable pruning (a couple of times a year) or a few such as the willows, you might be able to maintain them wih stooling (cutting to the ground periodically), though that will leave you with no screen for a few weeks each spring. Pruning 20’ plants is typically done with a lift truck; do you have the $ and access for that?

-Are deer an issue in your area? That is another consideration since favored plants may be eaten to the trunk, as high as the deer can reach, and lollipops won’t give much ground level screening.

-Are you looking for year round screening which would require an evergreen or something that grows so densely that even when leaves have fallen there is still privacy, or is a deciduous plant that only gives privacy during the growing season adequate?

If the neighboring house will be two stories, look at a narrower arborvitae/Thuja such as Emerald Green that stays uner 5’ in width, but still gets reasonable height. Or consider a fence for ground level privacy along with trees whose tops will provide privacy such as medium sized deciduous trees. They will fill much less of the ground level space in your yard.