I'd go with a linen/linen blend, no heavier than a sport weight, -or- believe it or not, a laceweight wool knit on larger needles. Wool knit up that way will wick away moisture and keep you quite cool and comfortable.
Just my opinion, your mileage may vary.
I'd recommend selecting a smallish range of fibers/fiber blends, and working up swatches of each to find the one you like best.
Enjoy finding the right fiber for you and knitting up the perfect summer top!