Every new city you capture, turn off taxing for them to help increase stability faster.
Everytime you win a battle take slaves.
Before sending our your fleet to blockade, append your 3rd army to it incase it gets attacked.
With control of italia, you gain more armies and fleets and since you gain a province you get to put up edicts which can enchance some stuff for you.
Once controlled you can choke the island with a blockade with your western fleet.
Attack the northern lands within the province of Italia ASAP as the opposing faction capital lies to the island to the west.
I'd wait until I have 3 or 4 armies first and if I can spare it a 3rd fleet. Try to have more, but they take up alot of income so don't build a 3rd fleet unless you can support it. One to the east of Italia and one to the West.
With rome, you need at least 2 fleets.
Your main army should have at least 3-6 melee, the rest ranged.
Lowers moral and weakens even the strongest of their units.
Use your spy to posion huge armies before attacking them.
That way the stuff mentioned above goes better.
Have one main army as large as you can followed by a 2nd army of medium size when attacking.
Having said that, don't do auto resolve on enemy territory, because if you did suffer alot of casualties you will have to fall back and replenish before advancing or you will lose that army quickly. Even with a high advantage you will suffer alot of casualties which takes a lot of time to replenish.
Don't use auto resolve unless you have a lot of veteran units and a 70%+ advantage.
Unless you are 100% confident you can take on the enemy army or you're a pro at battling it out. As Rome you need to be aggressive in your strategy.