Hi Arv!
This is a great question with a lot to think about. To start developing your essay, I would suggest approaching it in two steps. Before choosing the speeches you want to focus on, I'd encourage you to first choose three specific ways Shakespeare targets Elizabethan audiences through the plot and issues he raises in Hamlet.
Consider the big issues in Hamlet. Your prompt lists several possible aspects you could choose to focus on in this list (superstitions, hierarchy, social, religious, political, economic realities.) Which three do you think are most significantly paralleled in Hamlet's Denmark?
Consider what you know about the circumstances in England at the time Shakespeare wrote Hamlet. Since Hamlet is a story about who should and does become King of Denmark, and whether something has been done corruptly to change how power is transferred, consider the parallels you can find in Elizabethan England at that time, and how those issues might concern audiences then who would be impacted by changes in the monarchy. What was happening with Queen Elizabeth? What worries about the monarchy might be weighing on the public then? What if something similar happened in England to the power struggles Shakespeare portrays in Hamlet? Identifying the real life struggles or anxieties of the audiences of the time first will help you focus on which speeches relate to those audience anxieties.
For example, Queen Elizabeth was nearing the end of her reign when Hamlet was written. She was unmarried and had no children, and she refused to name an heir. There was a lot of fear in England about what would happen when she died. Hamlet reflects a lot of the worries of the people of England that the country could be thrown into turmoil and great instability if there was conflict over who would become the next ruler of England. Shakespeare dramatizes the impact of this kind of battle over succession by showing what happens when succession goes wrong in Denmark.
Once you have honed in on three specific issues audiences of the time were concerned about that are paralleled in Hamlet, you can more easily focus on the speech or speeches that address or relate to those issues. For example, which speech or speeches would resonate powerfully for Elizabethan audiences because they would connect to their own impending political fears about unjustified or rogue attempts to gain the throne following Elizabeth's death? What other issues on the list above are related to the worries on Elizabethans' minds? What devices does Shakespeare use to connect and reflect his audience's fears? What moral conflicts does Hamlet grapple with that could be parallel to those with which Elizabethan audiences also grappled?
I hope this helps! This sounds like a really cool essay prompt and Hamlet's issues over the peaceful transition (or not) of power and what it means for a society are just as relevant today as they were in Elizabethan times. Please let me know if I can be of any further help or if you have any additional questions!