I recommend an evergreen or semi-evergreen ceanothus for your border. Make sure you get one that is inclined to grow up, not spread on the ground. They are beautiful, the flowers delightful, good for bees, and most important you can prune them, train them into a little tree or tie them into a trellis, grows quite fast so you can buy a small one cheaply, they don't catch diseases in my experience .... easy!
Another easy win for your border would be a sambuca nigra, these are beautiful shrubs and again like being pruned hard and grow back fast next year. So if you mess it up one year you get another attempt! Also cheap. I've had issues with ants farming aphids on sambuca but still I think worth it.
Last recommendation is dogwood, to hide your fence. Lovely stems in winter. If you have a dark fence, a green stemmed dogwood would look stunning against it.
That border in your photo looks very shallow however. If you don't want to make it deeper, perhaps invest in a little trellis and grow a clematis. They need a bit of care but keep the label and follow the pruning instructions to the letter, you'll be fine.