cheapest and best way from Shanghai to JADE HOTEL in Beijing and cost please.

You are suggested to take a bullet train to go (with a second class seat).
From Hongqiao railway station, you can take a bullet train to BJ South. It takes about 5.5 hours and costs CNY553 for a second class seat.

When you arrive in the railway station, take subway line 4 (Daxing line) to Xidan, where transfer to line 1 and get off at Tiananmen East. Then the distance to your hotel is around 0.9mi. You can take a taxi to reach.