What i'm asking is if there was a particular ideology behind their wars, and if so what was it.
Political realities no doubt shifted over time, but Livy records the age-old religious process by which Rome continued to declare wars, he says, to his own day, which I would think counts as explaining the "ideology" behind the declaration of war. No doubt greed and however many other vices constantly played a great part in the actual decision for war, but the way that the Romans defined a casus belli in the eyes of the gods is described as originating with the quasi-legendary king Numa:
Numa had instituted religious observances for times of peace, he would hand down the ceremonies appropriate to a state of war. In order, therefore, that wars might be not only conducted but also proclaimed with some formality, he wrote down the law, as taken from the ancient nation of the Aequicoli, under which the Fetials act down to this day when seeking redress for injuries. The procedure is as follows: -
The ambassador binds his head in a woollen fillet. When he has reached the frontiers of the nation from whom satisfaction is demanded, he says, "Hear, O Jupiter! Hear, ye confines" - naming the particular nation whose they are - "Hear, O Justice! I am the public herald of the Roman People. Rightly and duly authorised do I come; let confidence be placed in my words." Then he recites the terms of the demands, and calls Jupiter to witness: "If I am demanding the surrender of those men or those goods, contrary to justice and religion, suffer me nevermore to enjoy my native land." He repeats these words as he crosses the frontier, he repeats them to whoever happens to be the first person he meets, he repeats them as he enters the gates and again on entering the forum, with some slight changes in the wording of the formula. If what he demands are not surrendered at the expiration of thirty-three days - for that is the fixed period of grace - he declares war in the following terms: "Hear, O Jupiter, and thou Janus Quirinus, and all ye heavenly gods, and ye, gods of earth and of the lower world, hear me! I call you to witness that this people" - mentioning it by name - "is unjust and does not fulfil its sacred obligations. But about these matters we must consult the elders in our own land in what way we may obtain our rights."
With these words the ambassador returned to Rome for consultation. The king forthwith consulted the senate in words to the following effect: "Concerning the matters, suits, and causes, whereof the Pater Patratus of the Roman People and Quirites hath complained to the Pater Patratus of the Prisci Latini, and to the people of the Prisci Latini, which matters they were bound severally to surrender, discharge, and make good, whereas they have done none of these things - say, what is your opinion?" He whose opinion was first asked, replied, "I am of opinion that they ought to be recovered by a just and righteous war, wherefore I give my consent and vote for it." Then the others were asked in order, and when the majority of those present declared themselves of the same opinion, war was agreed upon. It was customary for the Fetial to carry to the enemies' frontiers a blood-smeared spear tipped with iron or burnt at the end, and, in the presence of at least three adults, to say, "Inasmuch as the peoples of the Prisci Latini have been guilty of wrong against the People of Rome and the Quirites, and inasmuch as the People of Rome and the Quirites have ordered that there be war with the Prisci Latini, and the Senate of the People of Rome and the Quirites have determined and decreed that there shall be war with the Prisci Latini, therefore I and the People of Rome, declare and make war upon the peoples of the Prisci Latini." With these words he hurled his spear into their territory. This was the way in which at that time satisfaction was demanded from the Latins and war declared, and posterity adopted the custom.
This is all taken from Livy's AUC 1.32 in case you wish to investigate further, and I have selfishly lifted from this website to save myself the translation.
Rome has to have suffered some insult that is judged sufficient cause for redress by war, and the enemy is supposed to be given several chances and a period of time by which compensation could be made. At the end Livy indicates that the custom continued, but every indication is that it became more a system of formalities than of a real chance to avoid conflict, as when the fetiales began to save themselves the trip by designating nearby land as belonging to the enemy, making their complaints to it, and throwing the spear there instead of hiking all the way to an overseas enemy.
The theory of the 'bellum iustum', the just war, was quite popular in Republican times. It also means a bit more than a 'justified war', originally it meant more a 'war waged and opened according to the laws'. Cicero expands the whole concept a bit about it in de officiis and de re publica:
but our people have already brought all the world into their possession by defending our allies (sociis defendendis) [rep. III, 35]
This was one aspect of a just war. If you came to the aid of your ally, and beat the aggressor, annexing or pacifying some of their lands was justified. This happened often, since the Romans were in the habit of associating themselves with bilateral treaties with many sovereign entities all across Italy and the mediterranean, and, since Rome was since the fall of Veii and the dissolution of the Latin League the mightiest and most powerful actor on the Italian peninsula, other communities were often looking to Rome for help against aggressors. Of course Ciceros quote takes a few liberties with the interpretation of events, that the Second Punic War, e.g., was simply waged for the defending of allies is, ahem, debatable.
The Second Samnite War shows an example for this: Rome had allied itself with the Greek city-state of Neapolis (modern Naples), which was attacked by the Samnites (the earlier First Samnite War, which is probably apocryphal, saw Capua dedicating its territory to Rome to make Rome - bound by treaties to the Samnites themselves - help them defend against the Samnites). This, after a few early setbacks, led to Rome defeating the Samnites and establishing a bunch of colonies on their land. This process repeated itself often during the early history of Rome, ending with Rome controlling almost all of the peninsula either directly or via treaties.
Caesar, too, claims this frequently as a justification for war in his commentarii on the Gallic War, e.g. he justifies the first crossing of the Rhine, claiming that the Ubii had allied themselves with Rome and now wanted help against the Suebi (Bell. Gall. IV, 16 1-6). Cicero also justifies Caesars conquest of Gaul by saying that this was necessary to end the permanent Gallic threat to Italy's northern border, and this could only be accomplished by conquering all of Gaul, not only the tribes that directly threatened Rome, which already stretches his criteria for a just war quite a bit by waging a preemptive war.
Cicero also formulates some other criteria for a just war:
Those wars are unjust, which are undertaken without cause. For apart for the cause of avenging <oneself> or beating back the enemy, no just war can be waged [...] There is no bellum iustum without <first> threatening war, without declaring war and without demanding compensation (nisi denuntiatum, nisi indictum, nisi de repetitis rebus) [ibd.]
So, his criteria are these:
He also cautions that, even if injustices are suffered, revenge must not be inappropriate, the laws of war have to be obeyed, and negotiation takes precedence over force [de off. I, 34f.].
Earlier, the Roman concept of a 'just war' involved simply lawful declaration of war by the fetiales, the priests responsible for foreign relations: The fetiales would demand amends for suffered injustices (like stolen cattle, or land taken), res repetere, and, if denied, would throw an iron-tipped or fire-hardenend cornel cherrywood spear (the hasta fetialis) over the border into the enemies territory, which formally signified the beginning of hostilities and also a symbolic appropriation of the others territory. This type of behaviour was quite common for primitive societies in which cattle theft is the most common form of hostile tribal interaction (think of Homeric Greece). Later, when this wasn't practicable anymore, since the borders had been moved far from Rome, this symbolic act was move to the temple of Bellona. Edit: The above post by /u/QVCatullus contains a nice Livy passage describing the act.
This concept of a 'just war' was not without critique: the Greek philosopher Karneades argued that this was simply a practice used by the Romans to appear lawful while being unjust - this form of declaration of war observed the cultic formula, while violating morals. Cicero follows his critique in rep. III, 20:
How far utility has distanced itself from justice, the Romans themselves show, by having the fetiales declare war and legitimately committing injustices (legitime iniurias faciendo), they have brought the whole world into their possession.
This was at least the ideology behind it. The real aims and reasons were often possibly quite different.
It depends what era of Rome we are talking about
During the early republic era, the ideology was security. Warfare was common, and offence was the best defense for the Romans. They were a superstitious people and their success convinced them that the gods were on their side. The wealth the came from the conquests was immense and being able to profit while increasing security were good enough reasons to conquer. Once they became the regional power, Romans saw rival empires like Carthage the same way the Americans see Russia currently - a threat to their hegemony and security.
The ideology of the common people in the late republic wasn't what drove the conquests, rather the generals and politicians in the late republic were motivated by ambition and glory. When Crassus launched a competently unprovoked attack against Parthia Cicero declared the war nulla causa, without justification. Crassus didn't care, he didn't need any ideological imperative to justify the war he was launching, he had an army and wanted war for personal glory.
Then Augustus came onto the scene. He introduced an important ideology called the Pax Romana - the Roman peace. Romans had been conquering for about 200 years continuously, and Augustus managed to convince them that peace in conquered areas was more beneficial to Rome than additional conquests. After his time emperors would sometimes justify conquests by saying they were extending the roman peace to new areas. But still ideology was unimportant compared to more practical considerations such as the imperial treasury running low and a rich neighbors developing lucrative gold mines, as was the case with Trajan war against Dacia