If you lack a backyard, stick to containers. With the exception of some root crops and asparagus, most vegetables grow just fine in them. Tomatoes, green onions, peppers, beans, lettuce, and squash all fare particularly well.
Look for varieties bred to grow in confined spaces, such as Patio tomatoes, Topcrop green beans, and Bibb lettuce. As for what size container you need, use large ones (think whiskey barrel), which allow for companion planting and greater reserves of food and water. Small pots dry out quickly and don’t allow space for roots to grow. Whatever size you choose, make sure the container has holes at its base to allow for drainage.