From my experience, the bigger the better works for pots. I would also use the moisture control potting soil, or add moisture crystals. These will help you not to have to water as often. The ideal is to have the pots on a drip system with a timer. If not, I would have them all in the same area to facilitate watering.

The plants that you mentioned do very well in pots. Let each child choose what they want to grow, and let them be responsible for their own pot. Let them do research on growing their plant in Arizona. This can be a real creative experience. For instance, they may want to "decorate" their herbs or veggies with marigolds, which are said to repel pests. Or they can learn about companion planting, where growing certain plants together benefit both plants. Hope this helps. Virginia

A great resource is the vegetable planting guide for Maricopa County from the U of A Extension Office. A key to success is knowing when to plant certain vegetables. Okra, for instance, loves the heat of summer. Garlic is planted in the fall to grow through winter. Basil loves summer, while Dill loves winter. A neat winter plant for a large container is Fava Bean. Neat plant, and a great nitrogen fixer for the soil. You could teach your children some science with it. I have seen radishes grown in plastic shoe box containiers during the winter. Container gardening is a lot of fun. I agree with hoku, larger pots with moisture crystals. Mark your calendar for Saturday, October 21st. That is when the AZ Master Gardeners sponser their "Fall Festival" at Metrotech High School in Phoenix. Great event, lots of plants at good prices, and lots to see.

Here is a link that might be useful: Vegetable Planting Guide Maricopa County

Thank you both so much for the advice! I tried doing tomatoes and bell peppers in containers once before and had a terrible problem with pests. Is there something that is not harmful that I can use to deter pests or is there a certain variety of tomato that will be resistant to pests?

What kind of pests did you have? Hornworms? This year I planted an heirloom tomato "Pineapple", and it has no problems with pests. Seems to withstand the occasional hornworm. Past years they would devour the plants.

It was gnats and some sort of whiteish mold looking stuff on the leaves. I think it was due to me wetting the leaves too much but I don't know about he gnats. It was a mess. They were transplants from the nursery (tomatoes and bell peppers, I forget the variety).

If the whitish stuff was on the stems and if it was sticky, it was likely mealybugs and can be removed with rubbing alcohol, followed by a blast of water from the hose. The gnats feed on decomposing matter in the soil and don't really harm the plant. There's a nontoxic liquid I got years ago for fungus gnats that worked, but I can't remember the name. A Google search would find it.
Good luck!
Now if I can control these rabbits and javalina?!! A fence and pepper spray hasn't stopped the rabbits. The javalinas haven't noticed the fence either.
Norm