Carthage has all you need and you don't even have to think about cavalry too much. And you can throw in a few elites whose upkeep won't break your economy since they won't be coming to Rome from very far. Roman infantry is cheap and well armored. The best and surest way to deal is the typical frontal infantry engagement coupled with a cavalry charge to the flank or rear. Any other scheme takes too much effort and micromanagement. The Carthaginian roster's core mix is the obvious solution.