Answer: Wow -- a great specific question! If container vegetable gardening is something you plan to do in the future as well, I highly recommend that you get a book on the subject, such as The Edible Container Garden: Growing Fresh Food in Small Spaces by Michael Guerra. It suggests varieties and lots of helpful techniques.
Most of the crops you want to grow will do well in containers. According to the Southern Exposure Seed Co.'s planting calendar (they're located in Earlysville, VA -- http://www.southernexposure.com), August is the best time to plant broccoli in the Coastal mid-Atlantic region. Next spring you can start your broccoli in March for transplant. Broccoli prefers cool growing temperatures, so adjust the sowing time so the plants will mature during the cooling temperatures in October. You can calculate when to sow the seed based on the days to maturity listed for the variety.
Strawberries are perennial plants that will need winter protection. The plants themselves are very hardy, but their roots are used to the insulating effect of lots of soil, and aren't so hardy. Since yours will be in containers with their roots effectively "above the ground", you'll either need to insulate the pots on the deck with styrofoam or straw held in place with chicken wire, or store the pots in a very cool (35-40F) basement or outbuilding for the winter.
The rest of your crops are pretty easy, fortunately. Stay away from varieties described as having "vigorous plants. Look for "bush" or "container" varieties listed in catalogs. These have been bred to produce good crops while maintaining a fairly compact growth habit. For your vining crops, erect a trellis or netting for them to climb so they don't spill all over the patio. You will probably have to support ripening fruit (aside from the pea pods!) with slings made from panty hose or other fabric so they don't pull the vines off the trellis.
Good catalogs to peruse are Burpee (http://www.burpee.com), Shepherd's (http://www.shepherdseeds.com), and Park's (http://www.parkseed.com). I hope this gets you started!
Spinach needs cool temperatures in order to perform well, and not to "bolt" (go to seed). You can grow spinach in the cooler times of year, but for the summer, you can try Malabar or New Zealand spinach. These heat-loving greens aren't actually spinach, though they resemble it in flavor and texture. Also, choose lettuces labeled "heat-tolerant."
To stretch your harvest of beans, carrots, and lettuce, sow seed at 2-week intervals throughout the summer. Though carrtos and lettuce prefer cooler temperatures in order to germinate, once growing, they'll do fine. If you choose a quick-maturing melon, such as 'Minnesota Midget', you can also make plantings about a month apart to stretch the harvest. Enjoy!
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