You want a tree at the bottom left corner and perhaps another in that area on the left where the bushes.
Evergreen best if you want year round privacy. Some good not too big evergreen options:
Magnolia Grandiflora - flowering
Olive tree - delicate, good for near the house
Palms - if you like the tropical look
Photinia, Ilex, pittosporum, privet - look for ones pruned to lollipop shape as these are naturally bush shape
If you don’t mind deciduous there are loads more options - ornamental apple/cherry/pear trees are great for this and bring lovely blossom. Fig is very fast growing. Amelanchier. Sorbus or other rowan. Birch.
Paramount plants is a good website to help you see prices and narrow down options.
Our garden is smaller than yours and much more overlooked (3 storey terraced houses right behind) but feels quite private thanks to all the small trees we and neighbours have planted.