which shrubs / trees can you plant near the house?

My neighbours have all sorts of rubbish in their garden, old tyre wheels, indistinguisable large metal objects, traffic cones etc and yesterday a large wooden cot ended up there (the youngest is 15 so I'm not sure why)

So as you can imagine I'm desperate to plant something large which will obliterate our view of their garden. We've got high fencing, but you can look down on their garden from the bedroom, I thought if I planted something large there I would just see greenery instead! There was once a leylandi there which we had to remove as it was damaging our house, so I'm looking for something to replace it, does anyone know what will be tall and bushy and evergreen but not cause structural damage with its roots?
I was thinking about Cherry Laurel, does anyone know how far these should be from the house? Or is there a better alternative?

Help!