This is my first time visit my grandfather hometown in Longyan. Can any one help me which Airport

Yes, you can arrive at Xiamen Gaoqi International Airport.
Upon landing, take airport shuttle bus to get to North Railway Station. There are several high speed trains that can take you to the hometown of your grandfather. The train schedules respectively are 09:19, 10:16, 11:08, 11:29, 12:03, 15:28, 16:16, 18:27, 19:03, 20:24 and 22:02. It takes around an hour on the way.
About the ticket fare, first class seat costs CNY54.5 and second class seat costs CNY45.5.

May I know which is faster and easy to take bullet train , normal train or bus from Xiamen Airport

According to your requirement, it's suggested to take shuttle bus to go to North Railway Station. Then take bullet train to arrive. This is the faster for you to choose.