Sorry you've had no response, Natasha. This forum is pretty dead. Maybe try the shrubs, trees or perennials forums here on Gardenweb. They're much busier.

It would be nice if Houzz posted an 'Urban Gardening' cross link to here...I always seem to forget to look under S for 'Small Spaces / Urban gardening' and tend to look under U first.

Visually, I think it would look very sleek if you did only one type of plant all along the length of the box. Does it really need to be 2-3 meters tall? If so, I would recommend a vine, like clematis, provided its spilling onto the other side of the fence wouldn't become an issue with your neighbor. I am also seeing a line of hakone grass which might work at either the upper or lower level. I have no idea how either of these plants would do in your growing zone which is almost literally on the opposite end of the world from mine.

japanese maple green one can be kept under 3 by pruning,knock out roses ...

Hi! How much sun do you get back there? I have a small urban backyard too and I have almost all shade. I would suggest monitoring where your sun is at what times and what parts of your back gets sun. That way you won't waste your money on plants that need sun or shade and vis versa. That was my mistake!