Classical Greek Cavalry:
hippeus (pl. hippeis): The most general term in ancient Greek for cavalry (in non-military context refers to riders or even at Athens a census class).
hippotoxotes (pl. hippotoxotai): horse-archer.
hipparchos (pl. hipparchoi): Cavalry commander. (or for Sparta hipparmostes -ai).
prodromoi (pl. prodromos): Cavalry scouts or light cavalry. At Athens at least appear to have replaced hippotoxotes in the 4th Century BC and seem to have been considered superior horsemen.
Other Classical Greek:
Archers: toxotes (pl. toxotai).
Peltast: peltast (pl. peltastes)
But either of the above could also be called psilos (pl. psiloi).
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