E.S.
leaf lettuce does best IMO and it likes it a little cool so you may want to do it very soon. It can also take a little shade in the hot part of the day. It's roots are not thick or go deep so it doesn't need a really deep container. Radishes grow quickly and don't need much space or depth. Beans and cucumbers both come in 'bush' type that don't need trellising. Peppers and tomatoes do well but need deeper pots and lots of water. I have never put squash or zucchini in a pot, but I bet they would look great if you have the room for a bushy large plant.
Herbs also do extremely well in containers and love to be cut and trimmed for use. They just keep on growing and producing. Some of my fav. culinary herbs are basil, chives, parsley, cilantro, rosemary, oregano, and mints The first four are annuals and the parsley and cilantro often reseed. The others are perenials and usually do well if kept inside for the winter. The oregano and mints 'trail' like a hanging plant and do well in hanging baskets. I like them with either parsley or impatients in the middle of the pot and the trailing herbs around the edge so they hang down. (also nice in a window or balcony box on the railing)
Pansies and mini violets like 'johny-jump-ups' are edible and pretty too. (they also are good for strengthening capillary walls, therefore helping or preventing spider veins)
One neat thing to remember: If it tastes good together it grows well togeter. Companion gardening is awesome. For example; if you are growing tomatoes, grow basil around them. They taste good together and the basil and tomatoe naturally ward off things and critters that like to eat the other. Cool huh?