Really curious as to how big of an impact they had on Greece through out their years?
I'm also interested as to what made them rise, fall and grow a legacy that allows the word spartan to be what it is today.
Their impact was miniscule in the grander scheme of things.
Even as warriors they're not so awe-inspiring. The Thebans under Pelopidas and Epaminondas decisively and utterly destroyed them. Even during the Peloponnesian War the Athenians were able to match them more often than not, and scored notable successes. Athens was defeated by a long drawn out process and numerous unfortunate developments.
Though the Spartans famously rebuffed Alexander's threats with 'if,' the attempt of Agis to contest Macedonian supremacy ended in crushing defeat at Megalopolis against even the old Antipater. If the Spartans could not beat the ancient steward Alexander left behind in Europe, how could they hope to defeat Alexander himself?
But more importantly Sparta left almost no cultural legacy, most of what we know about Sparta comes from Athenian figures. What we know about Spartan Government is from Aristotle and Plato. What we know of Spartan operations during the Peloponnesian War is from Xenophon and Thucydides.
The last stand of Leonidas at Thermopylae was recorded by Herodotus, while the decline of Sparta and its fall to Rome is captured by Polybius and Diodorus. Even Spartan heroes we know of thanks mostly to Plutarch. If it weren't for Athens and a few other (non-Spartan) Greek poleis, Sparta would've been completely forgotten, ironically enough given that Athens was Sparta's bitter rival.
But I'd take Aristophanes and Aeschylus and Anacreon and Bacchylides and Callicrates and Phidias and Praxiteles over Cleomenes or Leonidas or Nabis any day.
Spartans were the human equivalents of silverbacks, tough in their own way, but still not as tough as popular history seems to imagine, and they've bequeathed to humanity almost nothing. Except a legacy for selfishness, brevity, and inefficient oppressive government that contrasts sharply with contemporary Athens or Thebes.
What you're getting at here I think is the "Spartan mirage", the question of whether the Spartans were as exceptional as they seem in literature.
I'm not sure how to link it, but u/iphikrates has an excellent answer in the FAQ (called Athens Vs Sparta I think)