Train from Beijing to Guangzhou with a break at Zhengzhou for a couple of days sightseeing.

I'm arriving in Beijing at 5.50 am on 28th February 2014 from Australia, and would like to take a train to ZZ city for a few days and the go on to Zhuhai via Guangzhou. I just read above that there is a shuttle bus from Beijing airport to beijing west train station, which I take it is the station to get the train to ZZ. What I need is a clue about: time, price and distance for the service to ZZ. Also some good inexpensive place to stay in ZZ would be helpful too. I'll be most appreciative for any help as a complete novice to China travel. Bruce, NSW Aust.