Flower pots and window boxes work beautifully for container gardening. Herbs grow particularly well indoors. Depending on your cooking style, one plant each can produce all the parsley, dill, thyme, basil and oregano you need for an entire season of meals. Follow the seed packet directions, or buy individual seedlings, and you're on your way. For the particularly frugal, ask a gardening friend or relative if they'll give you a few of their spare herb seeds.
Roots also grow well indoors.
Keep it moist but not wet in a sunny place. That one ginger root will multiply by up to eightfold. Replant one of the fingers and continue growing and regrowing for years. Garlic also grows well, but it needs cold temperatures to set the plant. Bring it out after a month or so, and let it continue growing.