I am deciding whether to take plane from Guangzhou airport to Fuzhou or Xiamen.

It would be beter to fly into Fuzhou, because it is much closer to your destination. around 69mi (106km), while XM airport is around 110mi (177km) away. After getting to Fuzhou Airport, you can take a direct shuttle bus to Putian City. Buses for this route are scheduled from 10:10 to 22:30. Upon getting to Putian, you can take a taxi to your destination then.

The air ticket fare changes a lot from time to time. U can search the exact charge on the flight page of this wesite. And the bus from Fuzhou Airport to Putian costs CNY52 and costs around 2h.