Initial thoughts..
What's your budget? I'd look into some nice paving (high budget) or pea gravel (lower budget). You could add some "stepping stones" or paving stones into the gravel for interest (either round, or rectangular/oversized for a modern look). You can often find this kind of thing on FB marketplace if you want to keep costs down. Secondhand bricks can also make lovely paths and/or "focal point" seating areas (I found some on FB marketplace and did this, for free)!
Then get some troughs/terracotta pots (again, look at FB marketplace for second hand if you're on a budget, you can get some great value bundles).
Tesco recently had some good value olive standard trees, so it would be worth checking them out.
Citrus trees generally need to be protected over winter in a greenhouse, so I'd steer clear.
I wouldn't varnish the fence (it can flake, particularly when applied to an old fence); I'd carefully stain it but do so very sparingly so that it doesn't bleed (and as others have said, establish whose fence it is first and speak to your neighbours, especially if the fence isn't yours... also might be nice to offer to refresh their side if it is yours - saves worrying about bleeds on the other side too)!
If you can afford to, don't be afraid to go big! Some large pots with large plants or trees would look great (keeping everything miniature can actually make a space seem smaller instead of enhancing it).
As others have said, climbers would be wonderful. I love jasmine trachelospermum as it's evergreen and has gorgeous smelling flowers. Be aware that you'll need a fairly decent sized pot as it won't be easy to repot it once it's climbing on the fence! Also reduces the need to water so often... I've recently moved away from using anything less than medium - large pots as the need to water frequently annoys me (and isn't great for the environment, but not so bad if you have a water butt - on my to do list this year)!
Edit to add... on the watering note, think Mediterranean. Olives, lavender, Mediterranean herbs, pelargoniums, some grasses, etc... this will suit your theme, look fab and be low maintenance on the watering front.