Do not re-pot even a poorly potted plant for its first few weeks in your home. Allow it to settle in to its altered environment first before making this stressful change.

These are shallow-rooted plants that like to be root bound in shallow containers. Re-pot when the plant is too crowded, as often as every year. Spring is the best timing for a quick recovery. The potting medium should balance moisture retention, drainage (especially important for Rex Cultorum Group begonias) and the need for stability. A classic mix recommended by the American Begonia Society is 1 part coco coir based potting mix, 1 part small (1/8 inch to 1/4 inch) size orchid bark and 1 part #2 or larger perlite.

Use a shallow terracotta pot with a drain hole no more than one size larger than the current growing container. Leave the soil lightly spread around the roots and do not pack it in firmly. Take care to keep the creeping rhizome above the growing medium rather than covering it or it will rot. 

While impractical in a home environment, the American Begonia Society also recommends moss baskets as a nearly ideal alternative for outstanding air and water exchange, consisting of a wire frame with long fibered sphagnum moss wrapping and filling it.