Carthage:
Focus primarily on economic buildings.
Only conquer what you have been given reason to conquer (raiding pop-up eleutheroi are a great excuse)
Only attack a faction after it has declared war on you
Accept a ceasefire always unless you are clearly dominating
Attempt to gain protectorates whenever possible
Maintain a strong fleet
Engage in diplomacy war with Rome for as long as possible (I have never had need of force diplomacy)
Mercenaries and subject troops are not nearly as important as saving your citizens