Could anyone please recommend a climbing vine for me?

I just moved into a house that in the backyard has some 7'-tall poles holding up a horizontal trellis. I'm going to add a vertical trellis between the polls and I'd like to plant vines that will grow up the vertical trellis and across the horizontal trellis to make a shady nook.

I live in Sunnyvale CA, near San Jose in northern CA, a Mediterranean climate (summers: mild temperatures but sunny and bone-dry; winters: cool with (at worst) occasional mild night frosts and frequent rain). The trellises are in an isolated, sunny spot.

My priorities for the vines are:

(1) Thick enough to provide shade.

(2) Not too thirsty (we're in a drought now).

(3) Easy to care for.

(4) Flowers (would be nice).

Thank you very much for your help.