At this point, Roman infantry tactics have developed over a few centuries from the hoplite phalanx which the Romans and other Italians used early in their history into the Roman manipular tactics that would later be further developed with the Marian reforms. At this point the Roman army was comprised of soldiers who were typically landowners, of varying amounts of wealth, who would fight and then presumably return to their crops. These men provided their own armor and weapons. The poorest of them (who also tended to be the youngest) were the hastati, who were more lightly armored and were the first line in the Roman army. Second were the Principes, who were typically older and wealthier and more experienced. They were more heavily armored and had better weapons. Then there was the Triarii, these were the wealthiest of the Roman soldiers who were initially equipped like the traditional hoplite with a spear, hoplon, and bronze breastplate but later substituted the hoplon for the scutum. Other wealthy men that could afford horses formed the Roman cavalry and were called equites although most of the Roman cavalry came from Rome's allies. Rome also had a lot of their allies serve in their ranks as infantry or skirmishers and they were called socii.

As for tactics, the roman army would form three lines. The hastati formed the first and if they couldn't break the enemy lines and force a rout then the principes would come second. If that failed to break the enemy line then the Triarii would be sent in. They would also be support by the socii and skirmishers while the cavalry would deal with the enemy cavalry. As for the Legionary tactics that you're thinking of, that didn't fully develop until after the Marian reforms.

Edit: I made a mistake, the hastati were the poorest not the wealthiest. Thanks to Kartoffelplotz for pointing it out.