You'll be able to purchase begonia tubers in the spring, and you can buy impatiens at local nurseries, or start them from seed - they're pretty easy.

The foliage of your begonia will die off eventually, after you've had a couple of frosts. Lift the tuber then, shake the soil off and store it in a paper bag in a cool place (mine are in the area in our semi-heated garage where we keep potatoes, carrots and onions). You can plant it again in the spring. Advice given to me that worked was to lay it a bit of soil in a container and as the foliage grows, gradually fill it in with more soil until your container is full. It will need to be hardened off after growing inside, but with your climate, that shouldn't be too hard, and it should be good to grow in no time. :)