What gardening zone are you in? That will help determine what you can grow if you want to maintain it in a container outside from year to year (whether with or without protection), unless you want grow annuals . Nurseries and big box stores sell trellises that are made to go into containers for training vines.

There are some blue or purple clematises, some of which are dwarf and/or can be pruned to keep on a trellis, and can be grown in a container. There are also annuals like morning glories, that bloom blue or purple, but they would need to be severely pruned and trained vigorously to maintain on a trellis and it can take some time before they bloom.