The trouble with 'quick growing' perennial climbers is that they are usually rampant too. They cover a big area quickly yes, but then they go on to cover a huge area just as quickly.
For annual climbers see if you can get seeds of Maurandia barclayana, comes in blue and pure white.
Otherwise you are into Clematis, Roses (yuck!) Solanum, etc.

Hi Steve, I love variegated ivies. They are very tough and don't grow as fast as the ordinary green ones. They come with large or smaller leaves, variegated silver or gold.
I like 'Glacier' as it has a large proportion of white/ silver/ grey, but there are over a dozen species and thousands of varieties. They're happy in shade too. I'm sure you'll want other plants as well, but pick a couple that you like and use them in a spot that would be difficult for more choosy things.

Steve, you need to consider the growing conditions as much as anything else - whether the area you want to cover is in shade, or gets a lot of sun, the soil remains damp or dries out, that sort of thing. You will also need to consider what kind of support the plants you choose will need - the only thing that will grow unsupported and cling to a fence is ivy, and virginia creeper (once it's got going, will need initial support). Clematis and sweet peas need thin supports to climb up, so the simplest answer is clematis mesh fixed to the fence - then there's the twiners, which will twine round a trellis section, such as honeysuckle and jasmine.
I'd echo Owdboggy's remarks about rampant climbers - unless you buy a machete at the same time, you'll have difficulty getting into your garden within a couple of years with something like, say, Russian Vine. I'd say the same about Jasmine officinale as well, much too large for a normal sized garden fence, gets 30 feet by 15 feet.

I'd recommend Trachleospermum jasminiodes for a warmer, sunny spot (evergreen, permanent climber with fragrant white flowers in summer). Otherwise Akebia quinata (doesn't mind some shade, but also needs a bit of sun) and any clematis which take your fancy - Hagley Hybrid and Nelly Moser do well in shadier areas.

hi Steve i have to warn you i put climbers on a part of my fence worse mistake i ever did i couldnt get at the bit to re preserve it and within 3 yrs had to replace a good part of the fence which rotted and the weight of the climbers pulled it over in the wind after i replaced fence i planted shrubs in front of it that way i can get to the timber to see if its needing retreated