best train or bus from Guangzhou EAST RAILWAY station to MACAO (or Zhuhai) ?

From the East Railway Station Bus Station, there are direct buses for Gongbei Bus Station, Zhuhai. Then you can pass the border to Macau.
The bus station can be found after you get out of the Exit H of East Railway Station.

there are a number of busses that leave for macau from the landmark hotel canton (which is also a very good hotel to stay at ) . The busses leave at various times of the day and can purchase tickets on the sidewalk from the bus operators . The hotel is located in the haizue? square (check spelling)