Pudong International Airport - 7am flight

Well, according to your departure time, no public transport is available. You are suggested to take a taxi to the airport directly. You can tell me the starting place. So I can find the estimated price and duration.

I don't have a hotel yet but probably near the people's palace. The other option I am considering is staying the night before near the airport?

From People's Square to PVG, the cab fare is CNY 250 to 260 at that time. You are share one taxi. Generally speaking, it takes around 40 to 50 mins on the way.
In addition, staying at the hotel nearby the airport is also a good idea. But you have to know that the airport hotels are more expensive than hotels in downtown area in general.