Answer: There are several considerations in planning this. First of all, how tall and wide will this hedge be? The Leyland cypress grows quite huge unless kept trimmed so it may shade your side. It also has an aggressive and spreading root system which will be proportionate to the size of the above ground growth. This may cause some root competition problems on your side.
As it grows, from a design stand point, the cypress should create a relatively neutral plain green backdrop for your own plantings. So it offers an opportunity to create your own vignette or pleasing scene on your side of it.
If you use all one kind of shrub for the entire run, you will accentuate the formality of the look. If you use drifts of several kinds of shrubs -- a drift meaning plant three, five, seven or nine of a kind in a loose grouping -- it will look less formal.
You could use another evergreen or several evergreens to create year round textural interest, or you could plant flowering deciduous shrubs, or you could use small trees. You could also use ornamental grasses. There is a huge variety of shrubs you could use, so in part your selection might be based on the considerations above.
For some interesting textural and seasonal interest you might try an evergreen with gold foliage such as a golden juniper (year long foliage color) along with a variegated red twig dogwood shrub (summer foliage interest, winter stem interest), and a rugosa or landscape rose (summer blooms, hips in winter) and possibly an ornamental grass (textural interest and drastic seasonal change).
You might also consider using a small growing tree such as smaller variety of crabapple or weeping cherry if you feel there is really space for that.
Another approach would be to build a pergola or trellis structure to help draw the eye, using the hedge as a plain backdrop, or to create an island bed closer to your viewing point to draw the eye before it even reaches the hedge.
Your local professional nursery staff may have additional or very different suggestions based on a more detailed understanding of the planting site and your overall design goals. In the meantime, I hope this gives you some ideas.
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