Guangzhou, shenzhen, putian.

No direct train from GZ to Putian. Here are two suggestions for you:
1. take train from GZ to Xiamen, and then transfer there to Putian. The train from GZ to Xiamen takes about 12 hours to reach. From Xiamen to Putian, there are lots of high speed trains. It only takes about an hour to reach. BTW, there is no special rate for seniors in train.

2. you can tke bus from the City Bus Station or the Provincial Bus Staion, or Haizhu Bus Station to reach Putian directly. Most of the buses start from the City bus station. The ticket fare is CNY270, and the journey takes about 12 hours.