Polly, container culture is certainly at home in the Cottage Garden! Part of the draw to the cottage style is that burgeoning, lush look, whether there is available earth to plant something or not. Begonias are among my favorites for my shady deck area, and for a few years I had great luck with Rex types. Last year our summer was extra hot and humid, and the heat came earlier than usual, so the Rex begonias didn't fare as well as in previous years for me. But I don't believe that will be such an issue in your part of the country. Most that I had were no id plants from box stores, but I do recall one I received from a friend called 'Color Guard' that performed particularly well. During the growing season they were easy to care for, I just kept them moist and fed them every couple of weeks, about the same as the rest of the potted plants.
For a couple of years I had good luck overwintering them too. They were particularly happy under fluorescent lights in a cool room with humidity trays under them. Some allow them to go dormant, and keep them on the dry side during winter. They survive that treatment without issue, but I found them very slow to rebound in spring.
I've been considering getting a few more this year. One of the problems I had was "the great cat explosion of 2009", when I had 3 females give birth! Let's just say that 18 kittens peeing in the pots is not good for Rex Begonias, LOL. I'm down to 2 spayed adult cats now, so it should be fine.
