For a lightweight 28 footer you could get away with 12mm but for most practical purposes choose 14 mm. Nylon is great as it stretches and so takes the snatch out but polyester is easier to handle and nearly as good.
Theb size of the rope will be limited by the size of the horn cleats you attach it to. Strength of the rope is not a real problem but bigger means more chafe resistance and simply looks safer. So as big as your cleats can handle. olewill