Roman expansion was generally not deliberate nor planned. Rome was a highly militaristic society, where glory and honour were paramount. The consensus these days is that Roman expansion was largely the result of aristocratic competition: persons from the elite (the senatorial class and perhaps equestrian class) vying for a limited number of magisterial offices (often involving military commands) and then using their time in office (which often was as short as a year) to get as much benefit as possible.

In war they could get glory, loot and slaves. If there wasn't a war, opportunities for glory were limited. It's not uncommon to see that a consul or praetor would provoke a war so that he could benefit from. There are also cases where a consul or praetor would sign a peace treaty just before leaving office, so that the next person in office couldn't benefit from the war (at least not that war).

None of what I mentioned so far has said anything about adding new territory to the Roman empire. It seems the Romans didn't care so much if territory was 'Roman' or not. They were often content to wield their influence over an area through diplomacy or local vassals. Only if there were repeated military problems would an area receive a permanent Roman governor (praetor) and legions.

Sicily was one of the first permanent provinces of the Roman empire. At the time it was important for the food supply of Rome and it was under constant threat of the Carthaginians, who previously held the island. That's why the Romans made it a province. After the Second Punic War two provinces were created in Spain, mostly because the local tribes could not be pacified. These provinces were created relatively quickly after the Romans came to the scene. If you look at (North) Africa though, the Romans were involved there in war (with Carthage) and diplomacy for many years before it became a province. Same goes for Greece: more than 150 years of Roman diplomacy (and hegemony) before it officially became a province.