I have looked online at schedules to go from Shenzhen to Zhaoquin

You must refer to Zhangqing. Well then, I checked that two trains leave from SZ East and two leave from SZ West. They are different from SZ Railway Station.

To get the train tickets in advance, you can go to any train ticket office in the city to buy upon the arrival day. Or book the tickets in advance through Travel China Guide!

Could also be Zhaoqing. Use www.chinatravelguide.com for your convenience.

SZ East railway station was previously known as Buji station, which is practical and on the blue metro line. SZ West railway station (Nantou) is a bit more tricky and best accessible via a metro/cab combo.

It would be recommendable to check a bus solution. Tickets can be bought at convenience in the Futian Intercity bus terminal Exit B1 on the green/Luobao/1 metro line, stop Zhuzilin. Some staff speaks English.

Best to show the Chinese writing to purchase tickets. Luohu train station also has an intercity bus station, as well as Shekou and several other spots accross town.

Enjoy the fountain city if Zhaoqing!