The flight ticket fare changes in different time with different airlines. Have no idea about the cheaper airlines. You'd better pay attention to the China FLight ticket website https://www.travelchinaguide.com/china-flights/ to find out a cheap way.
The nearest airport to singapore is Shanghai Pudong airport. If you take a taxi, the taxi fare would be more than CNY200.

Shanghai only has 2 airports, Pudong which handles mainly international flights and Hongqiao which primarily handles domestic flights. So your only option in this case is to fly to Pudong. If you are wondering about fares currently only China Eastern Airlines and Singapore Airlines offer non stop flights between Singapore and Shanghai Pudong. However, if those fares are too high for you then you may have to consider an indirect route via another city, eg. Bangkok, Hong Kong, Guangzhou etc. all have flights between Singapore and connections to Shanghai