SAGA or Lion Rampant seem like fine choices for games at the larger end of the skirmish spectrum.
For smaller-scale, if it's fast-play skirmishes that you're interested in then I don't think you can really go wrong with Song of Blades and Heroes, for which there's also Song of Shadows and Dust (more themed around urban conflicts in ancient times), and I
think a Song of Spears and Shields for ancient skirmishes in the works. Of Gods and Mortals is the same engine, if you want deities and mythological creatures and heroes.
7th Voyage seems like it could be used without modification, really, since there aren't character classes tying it specifically to Greek or Persian mythology. At its heart, it's just a very cinematic set of skirmish rules for a pre-Black Powder period, IMO, with lots of "sword and sandal" genre flavor heaped on top.
GW's LOTR is similarly adaptable, and you could easily cover this, or almost any historical period before the proliferation of firearms, with those rules. There are even rules for chariots in the skirmish game!
Might also be worth taking a look here:
http://freewargamesrules.wikia.com/wiki/Category:Ancients