what is the cheapest and best way to guangzhou airport from shenzhen Shekou?

You need to take subway Shekou Line to Shi Min Zhong Xin Station and transfer to Longhua Line to Shenzhen North Railway Station.
There are many bullet trains that can take you to GZ South Railway Station. You can take it.
After arriving, take subway line 2 to Jiahe Wanggang Station and take line 3 to Airport South Station, Exit C.