I feel your pain 
I think the challenge is finding climbers that are relatively fast growing but have year round interest and aren't too unmanageable (like Virginia creeper).
I have a selection of pyracantha (red/orange/yellow berries), golden and variegated ivy (less dingy than the plain green stuff), ceonothus (LOVE the blue flowers), winter flowering clematis 'Freckles', star jasmine, evergreen honeysuckle, passionflower and buddleia. I thought the last two would lose their leaves over winter but they've kept them surprisingly. The winter hasn't been too harsh but we've had a few frosts in the SE.
I'd try and get the biggest specimens you can afford to get off to a flying start. The buddleia, ivy and ceonothus grew the fastest in my case. The pyracantha are now looking good but took a while to establish. I neglected to prune them in to the fence to encourage new growth oops. Now rectified 
I attached reed screening to the new trellis while the plants established.
I also have a selection of spring/summer clematis, summer climbing annuals (e.g. sweet peas), climbing roses and so on to add a bit of interest throughout the year. I'm learning to layer my climbers 
If you have a lot of area to cover you could repeat climbers two or three times. For some reason when I started out I only bought one of each plant. I've since taken cuttings and have duplicates going on which is quite pleasant as you gaze down the garden.
I'd quite like to add a solanum and climbing hydrangea this year.
In front I have lots of medium sized shrubs and trees like acer, fatsia japonica, red robin, rhododendron, azalea, camellia (last 3 like ericaceous soil and feed) and smaller plants (perennials, annuals) for ground cover.
I don't know much about establishing hedges but hopefully someone else can advise 