If you want something really traditional you have to also identify which region you want your Nonna from, as tradition varies regionally. Around Napoli, I believe that a traditional sauce would likely be just be tomato puree. The flavours are those in the specific pizza e.g. a Margherita adding basil leaves, sliced mozzarella + olive oil. Or a Marinara adding garlic, oregano & olive oil. And perhaps basil.