I agree that it's a fantastic space full of potential and you definitely have some good 'structure' there to build on. "The annoying tree" looks like a bay to me, so it will be useful, and you can prune and shape it so that it is less "annoying" once you've had a good think about what you want it to look like.
The 'dead brambles' look like a climbing rose - do you know anyone who gardens and knows what they're doing who could help you to prune it properly? If not we'll have to see what we can do by remote control 
As for the sort of tree near the climbing rose, if it's alive it won't be long before it has some leaves on it, then we can work out what it is and what you can do with it.
As for what you can grow there .... do you like runner beans? Lovely fresh ones not the soft withered ones you get in the shops. Or maybe you prefer French beans (like bigger versions of the fine beans you get in the supermarkets)? Either would grow well there, climbing up amongst the other things already there, and giving the place a really lush tropical feel. You could grow some salad leaves too, and a courgette plant, and certainly some herbs. I think I'd grow some Morning Glory vines in there too - they'd look fabulous 