please what is the cheapest means of transport from Shanghai to Fuzhou?

The cheapest way is to take train K525/K163 to the destination at Shanghai South Railway Station. The ticket fare of hard seat is CNY128.5 and hard sleeper is CNY237.5. The trains take around 16 to 17 hours.
Personally speaking, the high speed trains are suggested. There are lots of trains that can take you to the destination in Shanghai Hongqiao Railway Station. The ticket fare of second class seat is CNY261.5 and first class seat is CNY333 . It takes around 6 to 7 hours.