shenzhen/dongguang/panyu/zhongshan

from Guangzhou airport, you can take subway line 3 to Guangzhou East to catch an intercity high-speed rail to Shenzhen.
Bullet trains (D types) are availble from Shenzhen to Dongguan.
Panyu is a district of Guangzhou, so you can take the D types from Dongguan to Guangzhou. and take the city bus to subway to Panyu.
To get to Zhongshan, you can still take the D types from Guangzhou south.