Two Examples of Inquiry Starters --these happen to be from/on Cymbeline, but this is for your review prior to writing the first Inquiry Starter on Richard III.

Example #1 of an Inquiry Starter (160 words): Majorie Garber's article about Cymbeline is interesting because it raises some key points about how the play functions as a "foundational text" for Britain. One of the key moments in the play that reminds me of this patriotic sense of British heritage is when Innogen is talking to Pisanio about leaving England, "Hath Britain all the sun that shines? Day, night, are they not but in Britain?..." It is almost as if in this section Innogen is hoping that there is something greater the world has to offer her besides her allegiance to her home country. This issue of patriotism is relevant when Belarius encourages the two boys to regard the ruling government with disdain, because the country will only betray them. I think it is interesting that Garber raises the idea that this text is a mixture of a history and a romance, and that the play has thematic elements that consistently question the patriotic feelings of the characters.

Example #2 of an Inquiry Starter (259 words): Colonization in Cymbeline
Though it can be argued that the treatment of Innogen in "Cymbeline", even as she was faithful to her beloved Posthumus, was written misogynistically (Cymbeline himself argued to who her body belonged and Cloten had some rather vile ideas about how to treat her) I was moved by the passage in McEvoy's chapter (238) that discusses colonization of the Americas as a way to view the character of Miranda.  I wonder then if the same cannot be said of Innogen?
All the men had different ideas for her: Posthumus saw her as a pure and chaste virgin (at first) that would be loved and cherished.  Posthumus, takes this news of a place/woman such as this (a near Utopia) to another shore and tells of this "virgin territory" yet unexplored by other men.  Upon hearing this, Giacomo needs to conquer Innogen himself, to discover if such a place/person exists, and bring back proof that there can be no such person, no such Utopia.  Cymbeline could be viewed as the ruler who wants to possess even this virgin country, this unsullied wonder and decide it's fate.  And Cloten wants to take everything he can from it, to destroy and rape the virgin land.  Of course I could go further into the analogy and perhaps talk my way into the whole idea of Utopia, but I think it is interesting to consider how Shakespeare's view was becoming so global and so political at the same time and using the tragicomedy as a way to explore a better world.