Abba_S: In my experience the boys family is contacted first and when they give a yes the girls family is contacted. Why this way? Because the shadchanim said so.
I am not saying your way is wrong or that the shaddchan doesn’t do that, just that after the boy says yes the girls doesn’t have much time to check references prior to the first date. Take time and the boy moves on to the next girl. The Shadchan because boys are in short supply wants to make sure he is willing before arranging a shidduch, otherwise it’s a waste of time.