If you are a beginning gardener and you want to grow vegetables, I recommend trying lettuce and zucchini. Both are easy to grow here in the St. Louis area, and neither one requires a huge investment in time or energy.
It's too late in the season to plant any more lettuce: I just harvested the last of the crop I planted last winter. Although technically I think you're supposed to wait until later in the winter, I planted leaf lettuce seeds in February and they did just fine, even though we had plenty of cold and snow. Once the seedlings came up, I fed them every couple of weeks with alfalfa meal and tried to keep the clover out of the bed. Other than that, not much maintenance is required. If you plant from seed, don't worry about neat little rows: when it's time to thin the lettuce you can eat the little plants you pull up.
Last year my first zucchinis ended up rotting on the vine (has to do with uneven watering and weird weather conditions), but the second round was pretty prolific. However, the continuous moisture this year means that the first round of flowers on my plants are actually producing fruit. I have two plants I got from a nursery and put in the ground two weeks ago, and each one already has a small zucchini. Several other flowers are blooming right now, so the females should turn into fruit this week as well.
I have been feeding my zucchini with alfalfa meal for the nitrogen, and Jamaican bat guano (available at Worm's Way) for the phosphorus. Phosphorus is necessary for good flower and fruit production. I don't feed on a particular schedule: just whenever I think about it, every other weekend or so. They are extremely prolific, and two plants should end up providing plenty of zucchini for two people for the whole summer.