Mrs P grows a range of things in containers very successfully - clematis, passion flower and jasmine. We don't grow but you could add climbing hydrangea and honeysuckle to that list. One of the great advantages of using clematis is the wide range of colour and flowering periods and generally easy pruning. I would choose well established and reliable varieties, those that have been around for decades. e.g Nelly Moser, Clematis montana. Another great plant would be star jasmine (Trachelospermum jasminoides).
Be aware different clematis varieties require different approaches to pruning. It's not difficult but important to get right. I would avoid having different types too close to each other to avoid pruning incorrectly. Google "clematis pruning types."
Thank you for the really helpful advice. Local nursery didn't have any Jasmine. My wife says she doesn't like the smell of Honeysuckle so that's out.