Answer: Since it is an apartment I assume you are thinking of inexpensive annuals. You should look for sunlovers such as marigolds, zinnias, snapdragons, sweet alyssum, cleome, tithonia, sunflowers, salvia, and verbena. Don't forget annual vines such as morning glories and nasturtiums. You might also consider some of the hardy (and non hardy) sun loving herbs which do well in containers (and in the ground). These would include: thyme, oregano, basil, pineapple sage, curry plant and scented geraniums. You might also consider some of the flowering bulbs such as dwarf lilies and gladiola, and some of the new tropical plants such as cannas for some added interest.
When you plant, be sure to improve the soil by adding lots of organic matterial such as compost, rotted leaves, or well aged manure and bedding to improve both the structure and fertility. Your annuals will also appreciate a few inches of organic mulch. For more information about annuals and container plants you might like to look at some basic books. Two I particularly like are "Annuals for Dummies" (ISBN 0-7645-5056-X) and "Container Gardening for Dummies" (ISBN 0-7645-5057-8) both by Bill Marken.
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