Squid is best cooked very quickly (in 2 minutes or less) or very slowly (at least an hour); otherwise, it becomes tough and rubbery. When cooking squid quickly, as in this recipe, remove the pieces from the heat as soon as they look opaque all the way through. If you can't tell, cut into one of the pieces to check its doneness. If it still looks translucent in the center, cook it a few seconds more.
A sparkling wine with very crisp acidity will balance the saltiness of the grilled squid. Try an Italian Prosecco.