What to plant?

At 10' we are really talking trees, and most of those aren't evergreen, nor do they conveniently grow quickly to that height and then stop!

The tree most people use in this situation is cypressus leylandii, which has a reputation like Staffordshire terriers, because unless it's looked after properly and given good discipline, it gets out of control and causes problems. I had 7 of them in my last garden, but not right on the boundary, so I could get all round and trim them every 18 months. They were kept at about 12' tall and no wider than 4' at the base and did the sort of job you describe beautifully. They took around a day to maintain if you count clearing up and disposing of the prunings, but a day every 18 months is way too big an ask for some (most?) people.

But if you don't think you will want to prune them or can't put them back from the boundary, forget leylandii and their slightly more sophisticated cousin, Western Red Cedar. Also forget Eucalyptus species, which are even faster-growing.

If you want this screen mainly for the warmer months when you are in the garden, rather than just looking at it from the house, then a range of deciduous trees could do a better job. For example you could buy 2 or 3 bog standard bare root silver birch for under £12 at present (but not in a month from now) and they'd do the job, or you could pay around £40 each for named varieties with prettier winter bark that would do the same thing in a classier way; rather like the difference between a Lexus and a Mondeo.

But, although they cast less shade than most, silver birch will not stop growing at 10' nor will you be able to trim them, so the garden will need to be large enough to take them when they slow down at around 20'.....or you'd need to hire a chain saw.

So, in short, some trees will get to 10'+ in a matter of 3 seasons, but they will keep going. There are many shrubs out there, evergreen and deciduous, that will also get to 10'. These are usually easier to manage than trees, but they may take 7-10 years to attain that sort of height, which could well be longer than you are in the house!