Dear Doug, Cool season, leafy green vegetables will be your best choices. Also consider herbs that like the hot weather. Radishes will work well too. Consider vegetables that do not "flower" and produce a fruit. Fruitinig vegetables require a long growing season, lots of water and nutrition.
Grapes will likely grow with the challenge of enough water to fill out the clusters during periods of extended dry weather. They are as they grow woody in natural and will need the support of the fence you mention.
Sincerely, Richard
