1543 BC - 1069 BC New Kingdom Egyptian (I/22)
A balanced, regular combined arms army with chariot Cv(S), bowmen and blades(F)
Might also work for Early Egyptian (I/2), which is similar but without the chariots
745 BC - 593 BC Kushite Egyptian (I/46)
Irregular army with lots of Cv and Bw.
Can stretch to Nubian (I/3) which is pretty much all Bw and Ps.
680 BC - 609 BC Neo-Assyrian Later Sargonid (I/51)
Strong regular combined army army. Includes Kn(S) chariots and plenty of Cv(O) or (S).
Can also be fielded as Neo-Assyrian Empire (I/45) which is very similar.
420 BC - 329 BC Late Archaemenid Persian (II/7)
Lots of cavalry and light horse, plus solid but unexceptional foot.
I have a bunch of Greek/Macedonian/Successor troops which can field several armies from 355 BC to 83 BC:
Alexandrian Macedonian (II/12)
Alexandrian Imperial (II/15)
Asiatic Early Successor (II/16)
Lysimachid (II/17)
Macedonian Early Successor (II/18)
Seleucid (II/19)
Pyrrhic (II/27)
Attalid Pergamene (II/34)
Later Macedonian (II/35)
These are regular, balanced combined-arms armies usually based on Pk, supported by good light troops and a handfull of Kn(F), Cv(O), LH and El. Early armies add Sp; Later armies replace or supplement Pk with Ax(S) and/or Wb(S).
225 AD - 651 AD Sassanid Persian (II/69)
Lots of irregular Cv and a few bits and pieces in support. Little infantry.
1066 AD Norman (III/?)
Irregular army of many Kn(F) supported by poor-quality infantry.