From hangzhou where should i go first before go to shanghai. Should i stay overnight in suzhou?

Suzhou is a great place to visit. Bus as I know, if you will go to Suzhou from HZ, you need to pass by Shanghai. So you are suggested to go to Shanghai first, and then pay a visit to Suzhou. Then bullet train from Shanghai to Suzhou only takes about 30 minutes and CNY59.5 for a first class seat, CNY39.5 for a second one.