China trip

Hello there,
We would like to take a trip to China for 2 weeks. We like to spend time in 3 areas such as Beijing then Shanghai, then to Hangzhou and Suzhou. Can we take the fast train from Beijing to those areas if so which one should we take, how much does it cost and how long does it take? Where should we go to see these sites?
Thank you advance,
LyLy,