I think you need to bear in mind that at some time or other the fence will have to be painted or coated with some preservative or other - and this could affect (or even kill off) things you plant very close to it. With that in mind, perhaps you'd be able to leave some space between the fence and any shrubs you decide to plant. If, for instance, you were to make two semi-circular beds - with the fence at the back of each one - it would mean you could leave enough room to get to the fence itself when you needed to.
If there were - say - a couple of fence panels between the two beds, you could attach some wooden trellis to the panels/posts to enable you to plant some climbers. The trellis could be removed to enable the fence to be painted - it could be supported temporarily whilst any painting took place and the climbing plants left in situ if they'd been planted some little distance away from the fence itself in the first place.