The Greek Military is highly dependent on the Political system of the Polis as well as your factions overall Skill Progress.

Oligarchy - Strong Elite Hoplites, no basic Hoplites
Democracy - Strong basic Hoplites
Tyranny - Heavy Cavalry, no Elite Hoplites
Monarchy - Strong Bodyguards, limited roster before Hellenism

Hellenism(High Tier Skill) - mainly benefits Monarchies, granting an array of Cavalry, Phalangites and Mobile Infantry, tho granting Oligarchies access to citizen Infantry is no small bonus.

In addtion they get (Greek and Thracian) Peltasts and Psiloi and some Factions get Unique Units that have their own set of conditions(see below).

In detail:
most Brigades are not government specific but can be trained in two Government forms like the Standard “Hoplitai” which can be trained both by Democracies and Tyrannies.
All Governments have access to Psiloi, weak slingers; Peltastai, light Infantry, once you have a Armoury; Thrakioi Peltastai, elite light Infantry, when mercenaries are availible and Epibatai, Marines, when you have a Harbour. With Hellenism this List is extended by Phalangitai, Thureophoroi(also needs Military Reform), Pezhetairoi(also needs Armoury) and Prodromoi(also needs warhorses).