Fighter is the most common class in the violent ancient world. Greek have specific commitment to warfare, as most citizen of the polis are considered soldiers in wartime.
Core Archetypes
Of the fighter archetypes, Champion is the most appropriated. The simplest Greek hero is a champion chosen by a god, bestowed with their power and glory.
The Battle Masters are especially appropriate for Sparta, the archetypical war-centered civilization. A battle master could be a weapon trainer or a successful general (a strategoi).
An Eldritch knight is a rare archetype in a greek world. Probably it could represent a Thessalian witch warrior.
A Purple Dragon Knight/Banneret (SCAG) would be used to model a noble warrior king, like Menelaus.
Both Arcane Archer (XgtE) and Sharpshooter (UA) are appropriated for an archer character. Archers are uncommon in the Greek peninsula; many came from the Anatolian peninsula. However, both Apollo and his sister Artemis are excellent archers, and their followers are trained on show bow. (Artemis is appropriate to match the fey flavor choices of the Arcane archer). Alternatively, you can reflavour those archetype as sling-based.
A Cavalier (XGtE) isn’t easy to adapt to a Greek Campaign. Probably, a Cavalier can come from the Thracian or Scythian lands, where the most skilled riders of the ancient world were born.
A Samurai(XGtE) is not very suitable for a Greek campaign, but you can use it to represent a noble Persian warrior.
An Echo Knight is an interesting concept for a unique fighter. It can be based in Narcissus, the beautiful hunter that fell in love with their own reflection in a pool of lake, if you are willing to assing a high ability number to Charisma.
If you ignore the psionic buzzwords, a Psi Warrior can be used as a unique, unsual warrior that can leap at great distances. You can reflavored it as a wind-powered demigod sired by Boreaus, the encarnation of the winter north wind.
A Rune Knight can be adapted to be a descendent of Cadmus, the greek hero that created the Phoenician Alphabet and founded Thebes. Alternatelly, you can reflavor it to be a son of the Gigantes, a proto-titanic race that was decimated by the Olympian gods.
Playtesting Archetypes
The Brute (UA) can be easily added to any Greek Campaing. Many of the bandits and brigands that antagonize the heroes in the Greek myths can be concepted as brutes.
A Knight(UA) analogue could be modeled as a Companion Macedonian rider, but even those won’t appear in history until the Hellenic period, later that the standard timeframe of Greek mythos.