Their initial troop is the Psilos, hopefully to gain a more suitably Linear B name in the near future. These are the youths and poorest of men levied into service - more than likely rowers who are raised to fight with what little they have with them - simple hunting bows, slings, perhaps some javelins, daggers and maybe axes. What you expect of men barely prepared for war - no helmets, no armor.
Tier 2 are the Damos, a term which is somewhat debated in application. Some consider it the precursor to "the people" in the later Greek Demos, others see it as simply a collection of landowning men or an analogy of a village. The use we're going with is something of a mix of the two, generally favoring the first cited definition. These are the common farmers, sailors, citizenry amongst the Akhaioi. They can be enlisted as skirmishers with javelin and sidearm, archers with simple bows and simple double-convex bows, or pikemen with tower or figure of 8 shield and long spear. None of them possess armor, but the pikemen are certain to possess simple boars-tusk or bronze helmets while the skirmishers are likely to have some, and the archers may have few if any.
Tier 3 are the Kekide, a term which seems defined as "Men-at-Arms", in this case being the retinue and entourage of semi-professional and professional soldiery for a man of higher station. Here helmets are guaranteed, as armor of some light sort. Currently there are two versions of the Kekide - a spearman continuing the classic tall shield and pike and an infantryman of the new style with lighter shield, long sword and javelins. It's possible the two will be merged into a spearman with sword, spear, and javelin.
Tier 4 are the Equeta, which translates more or less to 'followers', 'knights', and carries a noble quality with it. Some definitions place Patroclus as Achilles' Equeta, or all the heroes of the Iliad as the Equeta of Agamemnon. In our case I thought how all the kings of the Iliad had their own retinues, so that if Nestor and Diomedes were the equeta of Agamemnon then Nestor and Diomedes had their own equeta. Which is what these men are - the lower level of nobility in service to their respective kings. They wear medium armor of scale or even cuirasses of bronze, and fight exclusively in the new fashion with personal shield, sword, and javelin (with spears possible).
Tier 5 are the Promachoi. "Foremost Fighters", men fighting at the vanguard of the army, champions. In theory the major heroes of the Iliad are all Promachoi, but in our case the unit Promachoi are those once or twice named fighters who die a bloody death at the hand of a more important figure. Thus they are heroes above the fray of those nameless commoners slaughtered by the tens of thousands, but not high enough to warrant lordship. They are equipped similar to the Equeta, but with better or heavier cuirasses and an overall superior skill.
From Phthia one will be able to recruit Myrmidones, otherwise exclusively found in Achilles' army. They are a short and compact roster specifically tailored to swordplay and javelineering, being 3 to 4 tiers in total of exclusively melee infantry (javelin and sidearm, maybe spear). They are not "300 level" Superheroes, but they will be easily be the best melee infantry around. The goal would be something like the Nord Huscarls minus the armor-piercing axes (but with armor-piercing javelins!)
As for the cavalry: If we get a chariot script, then you will be able to upgrade Equeta into either Promachoi or Equeta Chariotry. I felt there wasn't a need for Promachoi chariotry because any heroic charioteer is going to be one of the lords. The Akhaioi like the Hittites and other Anatolians appear to have mostly favored the long spear and javelin in chariot warfare - bow depictions do exist in Mycenaean art but they appear rare. Hence the Akhaioi chariot would be a shock weapon.
hope this helps 
