I live in Baltimore and maintain lots of container plants in my 'concrete' backyard. I am also on my second year at an allotment garden plot (10' x 15'), through a program administered by the city. Ten yeas ago I wanted nothing to do with gardening, but I've really developed sort of a green thumb. Baltimore is blessed with good sunshine and usually good rainfall. I also water the vegetables in my containers with water collected in a basement dehumidifier, and flowers with dishwater after it's cooled (careful not to use dishwater after eating a meal that contained meat). Containers are a great way to get started, can be bountiful, and you can begin your new avocation in small steps. Begin with a couple or few pots, then add some every Spring as time and schedule allow. A few perennials, like strawberries, spearmint (think tabbouleh or sauteed with yellow squash or zucchini and garlic), and possibly rosemary will impress you with a return every year. Buy sturdy pots, good potting soil, and add some slow fertilizer to each pot, like bone meal. Water but don't over-water. Pay attention to the needs of your plants and move according to each container's requirement for sunshine.
Regarding edible plants, I recommend you start with herbs. I've only met a few people who couldn't grow basil and such. I transplanted a Genovese (or sweet) basil seedling from a big box store in 2006. The basil volunteered in the same pot the next year, and I've planted larger quantities of basil from seeds I gather from those plants every Fall. Don't discount herbs as merely flavorings, basil is essential for making pesto and Insalata Caprese.
Another suggestion is to try potting some strawberry seedlings. I planted several 'All-Star' variety strawberry seedlings (also in 2006) and have had them thrive every year, producing five or six dozen delicious strawberries every Spring. Be patient, sometimes strawberries need some time to 'pop', and a lot depends on the variety you select to grow.
Neither of these recommendations will put a ton of food on your table, but you are likely to grow them with relative ease. It's important to start small with plants that provide a pleasant reward. The treat of a handful of fresh strawberries or the aroma of freshly made pesto will inspire you to try something new in your container garden every spring. This year I am trying potatoes in containers (adding straw as the plants grow taller), leaf lettuce, scallions, cilantro, dill, and purple basil.
Best of luck and happy gardening!