Though remember that a hedge grows sideways as well as upwards, and will take a 2-3 ft slice off each of your garden edges. I'd consider either a higher fence/trellis with climbing plants or a mixed hedge of plants that you actually like.

Think hard about what you mean by privacy. I find that the illusion of privacy is adequate - I know people can see me (if they try hard enough) through my mixture of honeysuckle, clematis, roses and mock orange, but I can't see them, and that, I find, is all that matters.

Reserve somewhere in good light for your veggies and herbs - you'll struggle to grow them well if they're shaded. Consider growing fruit - tends to be more forgiving than veg. But also longer term, so it depends too on how long you expect to be in the flat.