Hmm.. a difficult one as there are not many fast growing evergreens that I can think of which would give you a quick response. Avoid Russian Vine like the plague or else you'll be lost within a couple of years within it's tendrils.
Clematis armandii is evergreen and you'll get lovely scented flowers in spring but it won't tolerate windy sites. Clematis montana is very fast growing and smothered in pale pink flowers in spring but it's not evergreen. Unfortunately I lost mine this year to a very severe frost early spring. You could mix one of these with a rambling rose or a jasmine officinale or even an ivy. Ivy comes in all sorts and doesn't have to be just plain old green.
Photo of an Ivy living with an Elaeagnus (don't know which one) which has decided it might like to climb with the Ivy so I've left it, topped with a Campsis (not evergreen but late flowering). See my blank bit of arch where the Clematis was - boo hoo...
Photo of the other side of the two together. They get a fair amount of shade from an oak tree during the day but they seem to like it. I think just greens works well.
Then perhaps a Kiwi. Not evergreen but is very fast growing and if you had a male and female you could get the fruit too (although I only have one and get little fruits so I don't know how that works)
I used to have a Solanum crispum on a trellis years ago. It went mad but I had the space to let it roam. Some winters it kept most of its leaves and the blue flowers were lovely all summer long.
Lastly, good old honeysuckle. Again not evergreen - although I do believe there is an evergreen now (?) and when in flower - as mine is now - the scent in the evening is devine.
Sorry this is a long reply but I hope it has given you a few ideas and you'll get even more help and advice I'm sure.
Enjoy your new home - and garden.