Look at the RHS website under plants. It will let you select shrubs by height and soil type and feature of interest. You can then check each one for spread, cultivation needs and so on.
Agree with KT53's comments re size of trees and garden dimensions. If you are determined to have something so high, it does need to be something finer and airier. Hence the suggestion for a silver birch. Do some research (library - books on trees) to try to find which might be the best variety to go for and perhaps visit a good tree nursery for some advice.
10m is as high as a 2 storey house so I don't really understand the comment that you don't want to shade the garden but you are considering putting something that high in? Planting a tree is a big step in any garden - especially a relatively small one - always think long and hard about what to use.
I'd be more inclined to go for perhaps 3 smaller trees (amalanchier / crab apples - these can still grow fairly tall and have seasons of interest) and some large shrubs which will give more of a feeling of enclosure and privacy and distract the eye away from the views
I fully understand why you want privacy from neighbours - but you are unlikely to be able to achieve this in the whole garden without making it feel like a prison yard. You could, however, probably make a secluded corner using (perhaps) a pergola type arrangement with climbers and large shrubs around. That way you will have an area to sit and relax / eat which is hidden from view but you are unlikely to be able to achieve that for the whole garden.
Most of us are overlooked by neighbours to some extent but unless you are trying to grow something illegal, it isn't usually a problem. If you surround yourself with tall trees you will have a very claustrophobic space. You can get a degree of privacy by planting trees away from the fence, maybe an apple tree or few which will give you blossom, fruit, and something to keep prying eyes from seeing you 24/7.
Rubi, trees or shrubs reaching 5-6 metres, 17 to 20 feet high can't be classed as small by any stretch of the imagination. In your original post you referred to them being used for screening which suggested that these would be a continuous line.
It seems that you have modified your original thoughts, and that's not a problem at all. It actually helps for making meaningful suggestions for practical solutions.
As for the effect on neighbours gardens. The sun isn't always high in the sky, and even when it is a line of trees (your original idea) would undoubtedly have cast a massive shadow over adjoining gardens. That's academic now as the ideas have changed.
I'd go along with the idea of a crab apple. It gives flower colour in the spring and wonderful autumn colour from the fruit. The fruit isn't poisonous, just tastes horrible, which might actually be a good thing with a young child. They might try it once, but never again!
Rowan (Mountain Ash) is another possibility, again good autumn colour from fruit and leaf. You'd need to check out whether the fruit is poisonous on that one.
If you're looking for something that will reach 15 to 30 feet in height, then you are going to get a fair bit of width with it too unless you go for a fastigiate form. https://www.rhs.org.uk/advice/profile?pid=117 Have a look at this site, fastigiate or columnar trees are near the bottom of the page, and it shows the eventual height and width of the trees in question. Many of them have decent blossom.