It really depends what area of Istanbul you'll be spending the most time in. If the Old City/ Sultanahmet, then I would prepare to stand out and deal with touts pretty much on a constant basis (they are very persistent, so be prepared). If you stay or hang out in the New City (over the Galata bridge) or Kadikoy/Moda on the Asian side, you can walk everywhere with no one bothering you or paying attention to you - it's wonderful. I spent over two weeks just in Istanbul (I stayed in an apartment suite close to the Old City) and would offer the following rule of thumb advice - the more skin you leave covered, the more comfortable you'll probably feel and the less attention you get as a young woman. And you will get attention, mostly because it's just not that common to see a woman traveling alone. And it will be obvious that you're a western tourist. The economy in Turkey is doing so poorly, I'm sure that there will be added pressure to engage tourists in purchasing all sorts of items you may not be interested in (carpets, trinkets, you name it - it's one giant bazaar).
So I would ditch any sleeveless dress or shirt unless you plan on putting something over it, which sort of defeats the purpose. I wore a bright sleeveless dress once and learned the hard way. So I opted for long linen pants and loose linen shirts and felt much, much better. I don't usually wear long skirts, but I did that as well. I was there in June too, so it was quite hot. Being covered up allowed me so much more (psychological) freedom - I could just walk into any mosque and tour it with no problem. And I just felt a lot more comfortable not showing legs or arms but just wearing light clothes that kept me as cool as possible. Don't overthink it...once you get on the ground, you'll get the hang of what feels better, but I would bring clothes you would not normally wear in Italy with you. I don't fully agree with the prior post that generally everyone is tolerant and cosmopolitan (it's all relative based on social class, whether religious or secular, etc.) - a lot of people in Istanbul came from very conservative rural areas and there is a very big divide between secular and non-secular norms. Plus there's an age and gender divide. Plus they have many poor refugees, so again, I would not assume that it will be like Western Europe everywhere in terms of very liberal dress norms. Given it's such a huge, layered city, you can experience all sorts of different "worlds" just in one place. I've seen everything from glittering high rises to really ramshackle neighborhoods where you will see only men sitting outside playing backgammon and other board games or smoking.