What you're trying to get at is what's usually referred to as "the legacy of Rome" -- and you could spend your life looking at just one slice of it; people do.

People make academic careers studying Roman architecture and city planning on the medieval (and even modern) city, for example.

Or Roman government.

Or Roman military organization

Or Roman law.

Or Roman poetry, philosophy and fine arts

Or the influence of Latin language on subsequent European languages

Or Roman patterns of trade and settlement on the subsequent development of the European states and economy.

Or Roman religion -- notice that the Pope is in Rome, speaks Latin, and has the same title ("Pontifex Maximus") as the Caesars had.

So there's any number of topics for you to choose-- but to write effectively, you'll have to narrow it down, because the "Roman legacy" as a whole, well, that's a big chunk of western civilization; if you try to tackle everything, you could easily spend the rest of your life on the subject -- an interesting life, but probably not your intention

Here are a few sources to get you started:

Basic

Traces of Ancient Rome in the Modern World - very basic National Geographic article, the level that would be appropriate for a middle school paper or such. Gives you the broadest sense of how people think of the the Roman legacy.

Advanced

Law

Influences of Roman Law and Civil Law on the Common Law

The Relations between Roman Law and English Common Law ... - jstor

The Importance of Roman Law for Western Civilization and Western ...

The Influence Of Roman Law In English Courts - Damien Freeman

damienfreeman.com/wp.../PDF38-Influence-of-Roman-Law-in-English-Courts.pdf

Architecture

The Influence of Roman Architecture on Modern Design | Design ...

21 Famous Buildings and Monuments Influenced by Roman Architecture

Art & Literature

Horace's Influence on Renaissance Epic

THE ROMAN CENSORS IN THE RENAISSANCE POLITICAL IMAGINATION

Roman Architectural Spolia

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. . . and so on. You could begin reading on "the Roman legacy" and continue for years.

So you want to narrow it down. Perhaps restrict your inquiry to the military? Rome leaves a legacy in military organization that exists to the present day: the way units are organized and commanded, strategies, responsibilities of officers and men, and much, much more. One place where Rome's military legacy is strong is the idea military engineering as an essential part of an army's function.

But there are any number of possibilities. Pick one that you're interested in, and dig in.

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