Imperator...
Welcome to the classic 4-Rome Campaign! This campaign is designed around Hard/Hard difficulty, and this guide will be tailored as such. Rome was not built in a day, and your campaign won't be either. This guide will simply focus on getting a campaign started. Anything too far in is too speculative to pre-plan for, though certain strategies generally apply to everyone's playthrough.
The year is 484 Ab Urbe Condita (270 BCE). 5 years prior, Rome had scratched and clawed its way to victory over one of the greatest generals of antiquity, King Pyrrhos of Epirus, and his formidable phalangites and fearsome war elephants. 3 years later, Tarrentum, the Greek satellite in the heel of the Italic peninsula, would surrender to the republic. In 270 BCE Rome is the overwhelmingly dominant force in Italy, with only a few remaining independent city states; the Bruttians in the south, and the rebellious garrison of Rhegium, who will soon be summarily executed that same year. Rome is on the cusp of securing total domination of the entirety of the Italic peninsula, and making ready to cross the straight of Messina into Sicily, make landfall on Corsica and Sardinia, and march into Cisalpine Gaul. The Republic is at a transition point from a regional contender, to the sole hegemonic power of the Mediterranean.
Your First Turn
We're going to get a cash injection right from the jump. We're only going to be using Arretium as a recruiting hub, so we'll get rid of (most) our recruitment buildings outside of that. Demolish the Basic Armoury in Volsinii, the Local Garrisons at Pisae, and the Training Grounds from Falerii, Volaterrae, Iguvium, & Corfinium. You should only have recruitment buildings in Arretium, and Cosa, which you'll need in order to train ships. This will give you a substantial cash injection for our next move investing in long-term growth. We want to set up as many crops as possible. With our newfound cash, build Crops in Falerii, Volsinii, Cosa, Pisae, Perusia, Sena Gallica, and Camerinum. Get Highland Pasturing in Teate.
Non farming buildings on turn 1 are going to be River Ports in Arretium, a Lumber camp in Reate, and Roads in Iguvium. The River Ports will turn Arretium into a trade powerhouse quickly, the lumber will allow you to construct ships, and the roads from Iguvium will help you move forces up through the Rubicon through Sarsina later down the road.
For troops, I try to get Funditores from Arretium, since your starting army only has ranged troops in the form of javelin throwers. Personally, I like to hit my enemies and know that they can't hit me back. Retraining troops costs Denarii, and more importantly, your time spent sending them back for re-training. Ultimately, the more you can soften your enemies before the melee combat begins, the better. In a typical army, I usually aim to have 4 or 5 archers/slingers to support the cavalry and infantry.
For conquest, we're going to take our starting army, led by Gnaeus Cornelius Blasio (who would go on to serve as Consul in 257 BCE), and immediately besiege Asculum. Sorry Picenum, but you have a recruitment building with a port that we need to build a navy in the Adriatic. Make sure that when you conquer it, you simply occupy the settlement. Enslaving populations is really only necessary when the native culture is non-latin, but with Asculum, Gnaeus may get the negative character trait "Enslaved Own Kin".
General Strategy
From here, don't advance too quickly up north. You're going to want to fortify you northern border with a full stack, while, building up an army to sail on over and capture Corisca and Sardinia. These islands will serve as safe means for you to fund your campaign into northern Italy, Cisalpine Gaul, and eventually the rest of the world, Jupiter willing.
Remember, use the Senate objectives as a good guideline for your conquest, but don't overextend yourself. Now go out there, and send the souls of the Gauls to Dis!
Senatus Populusque Romanus
RIS has re-introduced the Senate into the mod, and with that comes different strategies. While you will eventually reach the stage where you declare war on the rest of the Roman factions, that occurs too far down the line to be in scope for this guide. What is relevant to you is that the Senate will assign you missions. These include, but are not limited to: "Establish Trade with (Faction)", "Assassinate Target", "Blockade Port", "Capture Settlement", and "Establish Protectorate". It is almost always worth your time to complete these missions, as they grant you various rewards, such as "Increased Popularity with the Senate" (which will be key to advancing the main storyline), a lump payment of 5,000 denarii, or even a special recruitable unit. Not completing missions will decrease your standing with the Senate, which you can check by left-clicking the "Faction Summary" button at the bottom left, selecting "The Senate" tab, and switching over to the "Current Standing" option. There may be times where pursuing a Senate mission may not make sense for you to complete, e.g. capturing a settlement that would stretch your forces too thin to defend. You'll have to make that judgement call yourself, but just know that there may be instances where completing a Senate objective is not feasible.
"I spy with my little eye..."
Spies are one of your greatest assets. As you expand, visibility beyond your borders is going to be key to getting ahead of invading armies before they arrive. Spies also serve the purpose of helping you break into settlements extremely quickly. At spy level 10, having a spy in an enemy settlement will give you an 80% chance of opening the gates when you army besieges it. This means less time spent sitting in siege mode (opening your army up to counter-attacks & negative effects like dysentery) and more time conquering. Using multiple spies is an effective way for an army to daisy-chain capturing several settlements in a single turn. I'd recommend for starters that you have 3-6 spies out in the field before you leave the Italic peninsula.