Flat shoes or chunky heels! Many of the streets are cobblestone. You will get narrow heels caught in them.
Istanbul is a very cosmopolitan city. I would say pack a lot of interchangeable neutrals in dark tones, or however you would pack for a more western European city. Although Turkey is a Muslim country, you don't have to dress particularly modestly though you probably shouldn't attract attention to yourself with very short skirts or low-cut tops. (They do have a vibrant nightlife though, so some of this stuff is OK.) Bring at least one shawl to cover your head if you plan to visit any mosques. I'm excited for you! It is such a great city and has THE BEST food.