shanghai travel agent

What is the best/cheapest way to fly from Tai Pei, Taiwan to either Beijing or Shanghai?
I will be travelling from Tai Pei, Taiwan to Beijing and Shanghai in September. Which is the best/cheapest airline to use? I've heard that travel between Tai Pei and mainland China can be somewhat difficult. Are there any direct flights?
No travel agents, please.
There's no direct flight at all due to political reasons
Interest in Discovery of Shanghai city




