There are many threads on Poland on this Forum already. Give this a read...hopefully it's helpful. By the way, LOT Airlines flies direct from NYC to Warsaw, but last time I went I actually flew Finn Air through Helsinki.
https://community.ricksteves.com/travel-forum/poland/poland-in-september-2017
I am from Poland (Warsaw) but would definitely give Berlin the most time. Berlin is much bigger and has more things/sites to see compared to Warsaw. I could easily spend two weeks in Berlin (as a minimum, I would probably give at least 5 full days there, if not more). Warsaw, Krakow, and Berlin are of totally different scales: Berlin is biggest (needs most time), Warsaw (intermediate, at least 3-4 full days) and Krakow (very compact, at least 2 full days). You also have to factor in any side trips using these cities as your base. Warsaw is a very good base for train trips to other cities. As another example, while the city center of Krakow may not take a long time to see, adding Auschwitz and Wieliczka Salt Mines will increase the number of days because there is only so much you can fit in a single day. So when you're fleshing out the schedule, consider how you're going to spend your time, what you want to see, and any relevant side trips.