Is this best done as a class demonstration or a student experiment?

It's better done as a class demonstration during which the teacher asks open questions. 

Do you have any practical tips for carrying out the experiment?

Use a large flask so that it's easy for the students to see the solution and so that you can shake it vigorously. Don't forget to stopper the flask! The mixture can be reused for several hours.

Is the blue bottle experiment the only one of its kind?

No. There are other similar experiments using different redox indicators which involve different colour changes.