What is the easiest way to travel from Beijing to Hong Kong by high speed train?

I want to travel from Beijing to Hong Kong by G-type in October 2013. Is it best to go to Guangzhou or Shenzhen? Is it quicker and easier to get to Hong Kong from Guangzhou or Shenzhen. I believe I will need to change railway stations in both of these cities and then go through checkpoints to get into Hong Kong. We will have luggage but not too much.