I don't wear dress shirts, so I don't know much about that part. But I do have an opinion on wrinkle-free casual shirts.

I get laughed at every time I tell someone this... But for a wrinkle-free casual shirt, I really think the best bargain is the $9 Puritan from Walmart. Comfortable, no ironing and the colors last forever. You can travel for days in one shirt and still look fine (although you might smell, that's a different problem).