If you want to traval on a moderate budget from Shanghai to Beijing, you can take train. The detailed information can be checked at the timetable of Shanghai Trains(https://www.travelchinaguide.com/china-trains/shanghai-schedule.htm) . Weather of Shanghai(https://www.travelchinaguide.com/climate/shanghai.htm) in march is a little cold with an average temperature of about 5~13C.