The fastest and cheapest way is to take the subway.
From Jinzhou Metro Station, take Metro Line 4 (13 stops) to Chebeinan Station, then transfer to Metro Line 5 (5 stops), then transfer to Metro Line 3 at Zhujiang New Town Station. (Panyu Square-Tianhe Passenger Terminal) (take 1 stop) to Metro Tiyu West Road Station and transfer to Metro Line 3 (Tiyu West-Airport South) (take 12 stops) and get off at Metro Airport South Station. If you don’t use Yangcheng Tong, it’s only 14 yuan without discount, and it will take about 1 hour and 40 minutes.