Do I need to buy airline tickets prior to applying for a Z Visa?

We are teachers going to Shanghai from Oregon next fall. We have contracts and an invitation letter. Should we buy airline tickets now? Do we need to show our tickets for both ways to get the Z type, or can we go with a one-way ticket and leave the return open? How long after our teaching contract ends can we stay to travel? We'd like an extra 2-3 weeks.