Starting from Singapore, you could fly to Xiamen Airport from Changi Airport firstly. When you arrive at Xiamen, please take the coach leaving from the airport to Quanzhou City directly. The bus terminal is Quanzhou Bus Station where you could transfer bus to Nan'an City easily.

Xiamen Airport-->Quanzhou: buses leave the airport at 07:30~21:30, the journey is 1.5 hours and the bus fare is 45RMB per person
Quanzhou-->Nan'an: buses leave Quanzhou from early morning to 20:40, the journey is about one hour and costs about 10RMB per person

Hope this helps!