We want to go to Macau,Hongkong, Zhuhai and Shenzen this June. I don't know where to start first.

Well, since you arrive in and depart both from Macau, my suggested route for you is like this: Macau – Zhuhai – Shenzhen – Hong Kong. You can travel one day in Macau, and then go to Zhuhai. After visiting Zhuhai, you can take high speed train to Shenzhen. And then from Shenzhen, you can go to HK whether by coach or MTR train. After Hong Kong traveling, you can take ferry to go back to Macau.