Screening in your garden
One of the best instant screening shrubs is Photinia it can be purchase at a reasonable cost and if planted I well prepared soil it will grow away and increase in size quite quickly.
The best preparation is to break up the ground and dig in some well rotted manure or garden compost plus the installation of leaky pipe irrigation system simply laid around the base will help with watering.
Photinia can suffer from photinia fungus which causes leaf drop but this tends to effect plants that are struggling so plants that are feed and cared for mainly with watering in dry spells seem not to be effected by photinia fungus.
Using small hedging plants as insurance to secure the side hedge
With the rose on the lefthand side as you look out of the house. As the rose is quite large and will tend over the next few years go bare in the base allowing you to see through to next door.
One solution to this is to buy some small pot grown hedging holly (Ilex aquifolium) and plant them into the base of the rose. As they are quite happy growing in shade they will establish and fill and gaps in the lower part of the hedge formed by the rose.