We are an art school and we have teachers and student groups that would like to have their own wiki. The question is, do they need to create their own wiki and unique wiki name, or do we/they create a specific page on the main wiki site?

This really depends on the needs of your students. A free, individual wiki has 10mb of space for you to make wiki pages and store uploads (like photos of art projects, etc.) and free educational ones are the same.

So while having 1 free wiki with everyone's stuff on it would probably fill up fast, if you had the funding to pay for a Premium wiki, you would have a lot more space for everyone's group pages, and they would all be on one wiki. So again, it's up to you and how you want to organize your wiki.

If you choose to have several wikis, I recommend having one main one that links to the the group wikis, and make sure to have the group wikis link back to the main one.