The OCD, following Casson's superb books on ancient seafaring says that sails in the Mediterranean were made of linen, and adds that leather was often used in the corners or in strips to strengthen sailcloth. Besides that, what sort of sail a ship might have depends entirely on the sort of ship--there are several different kinds of galleys, and most ships were not warships at all, but the large cargo ships that sailed without oars, propelled only by sail. Square sails were the most common on all ships, but the OCD mentions triangular sails and lateen sails both, along with spritsails and lugsails. I don't know enough about ships to know what those last two are, though :/