I suppose it depends on "casual" and where you want to wear the shirts, but for travel in warm/humid climates, my husband loves fishing shirts - Columbia makes them, you can get them at Sierra Trading Post, REI, Cabelas etc. Wicking fabric, lots of pockets, vents in the back, and they don't wrinkle too much (any wrinkles fall out quickly in a steamy bathroom or in humidity....)
I got him a couple of these for his birthday recently and he loves them:
http://www.sierratradingpost.com/red...colorFamily=07
He has some of the Columbia long sleeve versions, and a short sleeve from Gander mountain.
I should note, my husband really doesn't like a polo/golf shirt with knit collar. Prefers a silk Tommy Bahama, but for more casual (hiking, day trips etc) the fishing shirts are hardier and more practical....