"The family waits for the postman."
Translation:A família espera pelo carteiro.
Because "para" is the forward/going to word. We have a gift for her, but it is to give to her. If we buy a gift to give to someone else from her, then it is for/on her behalf (por).
Well, we may be looking forward to seeing the postal carrier, we are not waiting to the mail carrier but, rather waiting because of the carrier. So "por" is the best choice here.
These will help,
Por vs Para:
PT Help Index: