Personally I'm a big fan of 7th Voyage by Crooked Dice.
It's really aimed at recreating the feel of old sword-and-sandal flicks with claymation monsters, like Sinbad & Jason & the Argonauts, so it doesn't have culture-specific army lists like Greeks, Persians, Celts, etc. etc., but it does have a lot of flexibility in unit and warband creation, and lots of monsters.
Rather than picking a faction, you're either heroic (with a couple of leader types like the champion or dashing rogue) or villainous (evil mastermind and vile tyrant), and various supporting unit types like brother-in-arms, "villain's right hand", etc. fill out your roster. Lots of monsters, too, so the mythology angle is pretty easy to replicate.
If adapting LOTR SBG, there are already historical lists for Romans, Celts, Germans, & Dacians (the latter three are all pretty similar), and a quasi-historical Greek list with some mythological elements. Add those to the wealth of profiles that already exist for that game and could be "counts-as" basically anything you want from mythology, and I'd say you're set to go.
One last game that I've never played, but also seems to fit your bill of ancient mythical skirmish poutpourri would be Broken Legions. It might veer a bit away from "mythical" into more modern conceptions of fantasy, though, as I believe there are vampires and werewolves and such. Anyways, maybe worth a look!