Rome at it's start was heavily influenced by the Etruscans, a more advanced and powerful culture to their north (even controlled by a few Etruscan kings at some points). The Etruscans themselves were huge into Greek culture and imported things from the east by the boatload. So no surprise that the Greek hoplite system made it to Etruria and then into Rome.

Early on Rome was merely one of many Latin cities located at a key crossroad. In the century after the founding of the Republic it slowly won hegemony over its fellow Latin states and even conquered a powerful but nearby Etruscan city that had contained it. In the 4th BCE Rome got involved in a series of wars with the Samnites who lived in the hilly interior of Italy over who's going to be the top dog in northern/middle Italy (the Greeks held the south). Obviously a hoplite phalanx isn't going to perform well in the hills so they adopted the manipular legion, based on the Samnite fighting style. Since a soldier was an individual swordsman, a tower shield was better for protecting his person rather than the bigger and heavier aspis of a hoplite.

Reasons for the conquests were varied, some of it was outright opportunism, others were defensive struggles - they just happened to be better at it then everyone else. Part of this success came from their incorporation of each defeated state into their army.