White is the perfect color to wear in the summer. It reflects light rather than absorb it like darker colors do, and so a white garment tends to keep you cooler than a dark one. How cool it is also depends on the fabric used, of course. Look for lightweight fabrics that let air flow in and out. Heavier fabrics may trap your own body heat. Beach shirts are often made of linen, while Hawaiian type shirts are usually cotton.
A couple of examples I find quite casual and nice:
Mens white beach shirts:
Mens white beach shirts pictured:
Left: Hawaiian Aloha Fashions White Wedding Men Hawaii Island Shirt
Right: JMP Cotton drawstring collar long sleeve beach shirt
Keep in mind that linen wrinkles easily, and that is partly why it is a fabric used in casual garments. It does have that summery, beachy look, though. Of course, almost any shirt could be considered a “beach shirt”.