Answer: The veggies you've listed will all grow well in 3 to 5 gallon containers. Make sure the pots have good drainage, and fill them with potting soil or a mixture of one-half garden soil and one-half potting soil. (If you use straight garden soil it will be quite heavy and can dry out completely, making it almost impossible to rewet again.)
Veggies grow best in all day sunshine. If you can only provide 5-6 hours of direct sunshine, try growing some of the shorter season varieties. They can get along with a little less sunshine than their longer-season cousins.
Try 'Blue Lake' beans, 'Short & Sweet' carrots, 'Sugar Crunch' cucumbers, 'Early Girl' tomato (or 'Sugar Snack' if you like cherry tomatoes), and 'Richgreen Hybrid' zucchini. Be sure to provide some support for the cucumbers, squash and tomatoes!
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