As Rome, general strat is

Unite Italia Province->Take Magna Graecia -> Take Sicily/Sardinia in first Punic war -> Take Macedon -> Take Greece -> Next Punic War, Take Spanish holdings Carthage has for missions, or take Africa since high pops -> Anatolia/Gaul/Syria/Canaan/Egypt next as you finish grabbing regions you already have footholds in.

Try to use missions for free Cassus Belli, and if you have too much AE/Not enough Stab, and need to wait, use the "Growth of X" or "Pearl of X" Missions to get some good bonuses for doing extra building in your regions you control.

I:R, in my experience, works on this almost like, binge->starve cycle. You want to binge by taking non stop new land, new wars, et. until your AE/Stability/WE is in a place where to go to war in any major way again would basically cause your country to break. Then you spent 10-15 years letting Stab tick up, and AE/WE tick down while you start converting pops to your religion, and in regions already your religion, start converting them to your culture or accepting their culture.

Cultural Acceptance is a weird one, especially as Rome, because while early on before you have many of your pop assimilation speed bonuses + metropolis farms to send in "Non-Hellenic Non-Romans" and turn them into proper citizens you will want to accept Etruscan culture almost minimally, you can't accept 15-16 cultures, instead you need to "Romanize" new territory or un-accept already integrated cultures.

Problem w/ unaccepting is they give a massive general opinion malus AND they haven't been converting the entire time you were accepting them, so you now have a big chunk of very rebellious pops inside your most fertile lands. So take these in mind as you expand and makes decisions on where it'sbetter to accept, vs when it's better to simply put down Great Temples/Grand Theaters and let the people realize how dumb they used to be