What kind of visa must we apply for, and what additional documents are needed?

To my personal understanding, I think you need to apply for the Z type one. In order to apply for it, you first have to get the work permit. The university should help you acquire it. I don't if you have signed contract with the university since you just work there as volunteer. The work contract is needed when applying for the work permit.

I think you'd better consult with the Chinese consulate in your area. They might advise you what type you should apply for.