My army as a roman general would at the beginning of the campaign be mostly hastati, equites and generals plus a few velites. Those are good enough to take Gaul, Carthage, Greece and Macedon. By that time you should have some principes, archers and some more cavalry, plus mercenaries.
No matter which family you play, from there on I use more cavalry and archers because:
Scipii face Numidians, who have mostly missile inf and missile cav, so I take lots of archers and cavalry to deal with them.
Julii face spain and britons, so take some archers to deal with chariots, you dont require anything special to beat the spanish. I find that barbarian mercenaries are good for absorbing chariot attacks, just make sure they dont break.
And in the east you'll be facing dacia, trace and pontus, and in my case usually egypt too. Dacia is best taken out with a balanced army with as core heavy infantry. Against Trace it would be wise to have some archers to deal with those annoying milia cavalry.
Pontus only good units, except for phalanx are all cavalry and mostly throw stuff at you, so keep some archers ready to hold them off and some cavalry of course.
Egypt has too much chariots to simply eliminate them with archers, so be sure to have enough infantry with good morale. And they have a lot of archers, including the excellent pharaoh bowmen. To deal with these and to flank the spear units have a large number of cavalry ready, but hold them behind your line untill the chariots are locked in combat, cause you dont want your cavalry running into their chariots.
Against Parthia you'll barely need infantry at all. Just some infantry to protect your archers and lock the eastern spearman in combat.