We want to cover the side of our house with a nice evergreen but need advice

I hope you didnt pay for this poor rendering job. I personally would hack it of, and have it properly rendered. Ivy seems to be the fastest growing and most popular, but keep it trimmed when you have desired height. In my opinion I wouldnt grow anything on the walls, only suggesting ivy, as your question is, what can I grow on the wall.

Plants covering walls can actually benefit in two ways. They can reduce heat loss in winter as well as aid cooling in summer. In both instances by providing insulation. Proper training will not encourage damp. And if the right plant/s is/are chosen they are stunning. In your case, it really depends on the aspect of your house. In which direction is the wall you would like to cover facing? Magnolia grandiflora has beautiful and impressive large flowers, glossy evergreen leaves upto 20cm long, and can tolerate some shade. Needs shelter and not dry (perhaps near downpipe would suit). Needs to be trained against the wall (not self adhering like, for example, Ivy). For a south or west facing wall Trachelospermum (Star Jasmine) would suit. It does need shelter, free draining soil and a good feed.

you can do this if you use the right climbers not ivy it will distroy brickwork/render try you to use climbing roses or clamatus which will not harm the brickwork etc malc

I would not recommend putting any plants to grow against a building as it may encourage damp and vermin. You will not be able to maintain the building. the best thing is to have the wall re-rendered. Go back to the company who rendered the wall and ask them to correct it or tell them they are liable for rectification.

I agree with jmb, after recently stripping a wall of ivy, the plant caused some serious damage.