Do I buy the flight and then just get visa at the airport or buy flight and visa at HKIA meanwhile?

Joanne, just buying the flight ticket to Shanghai is not enough. If you do not have HK residence permit, it's hard to say whether you can get the mainland entry permit. If you do want to be in Shanghai tommorw, the only choice shall be buying a flight ticket from HK to Shanghai and then to a third country so that you can make use of the 72 hrs free transit policy. However, by doing so, you can only stay in Shanghai for three days or so.