I don't want to suggest any answers here, as the essay is yours to do, but I'm happy to try to help with thinking about what questions to ask. Thanks for being upfront about the nature of the question.

Yes, these questions really don't seem to have been posed from a military history angle.

A lot's going to depend on what you interpret as "glorious", and that's a very subjective thing. It's specific not only to your culture but also to your politics, your philosophy, and perhaps even your religion. What an atheist libertarian art historian regards as "glorious" is likely to be very different from what a Muslim socialist theologian thinks. So one central problem you've got to deal with is that the core term in the question is subjective to the point of being meaningless.

To come up with a good answer, you're going to have to come up with a sane, well-reasoned and well-founded way of interpreting that word. Don't skip this step. It's important.

The other part of the difficulty is the research you choose to do. You suggest "uniquely classical Greek military tactics" etc. that are still in use; that's one possibility. But it's probably the absolute hardest possible way of approaching it: we don't really know as much as we'd like about Greek military practices, so you'd basically need to do a PhD's worth of research, and read many weighty tomes on both ancient and modern military theory, to have even a chance of succeeding with this angle.

I'd suggest it might be more manageable to research the impact of Greek military matters on, not just military theorists, but also politicians, teachers, and ideologues. (Military academies still have classes on events reported by ancient historians like Thucydides and Xenophon: why?)

And it doesn't need to be just about military practices: military persons can also take on a meaning of their own. Take one example: Alexander the Great reportedly modelled certain aspects of his public identity on the mythical hero Achilles . Who does the same with Alexander the Great now? And why? What meanings has his military career taken on in recent times? (If you know anything about the relationship between Greece and the Former Yugoslav Republic of Macedonia you'll find a lot going on there.) That's just one example of course. In the popular imagination, there are other figures that are as much symbol as they are history: in one well-known recent movie, Leonidas was used to fuel a libertarian and nationalist agenda, and even to argue in favour of a specific military action. "Glorious" or not, ancient Greek history still has an impact on public discourse. Does that make them worth studying? Well, that bit I'll leave to you.

Just dovetailing off the good suggestion above, I will suggest when writing this essay to use a few Greek authors to answer the ancient military history question you think of you. If you have the time, reading a couple books by Xenophon, Thucydides, Demosthenes, Isocrates, or Herodotus would really tie together another ideas that come from other research materials. Then after this you can see why they thought Greece was glorious and worth fighting for regardless of the opponents they were facing (since this was the point when war was rampant and against difficult opponents). This theme of fighting for Greece because of her past glory and possible future glory is a theme that comes in Xenophon’s Anabasis, Hellenica, and Cyropaedia. Also in Thucydides’ The History of the Peloponnesian War and Herodotus’ The Histories. Then lastly, in Demosthenes and Isocrates’ prepared speeches that were written during the late classical period.

It would be good to explore a couple of these texts of your choice because all of them say why Greece is glorious and worth fighting for. This will give you a good historiographical answer you can use in your high school research paper your teacher will probably like to see. Additionally, using these sources in your paper will help you see the Greek opinion of war and highlight Greek virtues shown during war in battles, diplomacy, and other situations. This will then give you a chance to answer the second part of the essay prompt easier since you have related with the ancient Greeks and can compared their military values and virtues to ours. This is not an easy based on the prompt you are given but by looking at these primary texts I think it will be easier for you.

you could perhaps say that the Greeks are the first examples of campaign narrative. Xenophon is essentially a running account of a campaign remembered later on and his style influenced everyone. Alexander took the Anabasis with him to Persia, Julius Caesar wrote his military accounts in imitation of Xenophon and there are echoes of him in the Campaign diaries of Sulieman I (although i would check another source to make sure on that). I dont know if that's too literature focused though.