You can have the pots inside or outside, they don't require weeding, and can really brighten up a home. The most important consideration is the size of the pots. Get pots large enough so you won't need to water constantly, but small enough that your children can move them around. You can also create flower pots by cutting open old milk jugs or other clean plastic containers. Remember, you should only put one plant in each pot, to allow for proper growing room.
Geraniums are hardy and work well indoors and out.
Another good choice are chrysanthemums. They flower often and can be outdoors. Let your children pick out a few plants that appeal to them. Growing an herb garden is a delightful alternative to flowers. Herbs do not need a lot of sunshine, and they don't care about the quality of the soil.