So this is a really cool question that I like a lot. I’m going to use part of the thesis I’m writing for my M.A, because it has a lot of good information on this topic. It is not necessarily perfect for developments in the first and second centuries, but should provide really good insight into the major turning points and how the army developed during the third and fourth centuries.

In summary version, the armies of the early Empire, the first and second centuries, were stationed entirely on the frontiers of the Empire’s territory. As controversial military-strategist-turned-historian Edward Luttwak puts it, this was something akin to ‘forward defence’. Ideally, the Roman commanders would be informed, usually by deserters or spies, about outside threats and barbarian armies that were forming. They would then prepare an expeditionary army by requisitioning vexillationes, which were detachments of about 1,000 soldiers, from other parts of the frontier. This would create a field army large enough to campaign against these threats. This system also worked for offensive campaigns, for example during the Dacian Wars the main legions were brought from Germania Inferior and Raetia and a vexillatio was brought from a legion stationed in Judea.

This army was comprised of two elements, the legions and the auxilia. There were 28 legions under Augustus (27 BCE-14 CE) and they were recruited entirely from the citizen body, sixty-two percent of which were from Italy. Each Augustan legion had an 'on-paper' strength of 5,120 men, meaning the official size of the combined legions was 140,000. Supporting the legions was the auxilia. Roughly numerically equal to the legions, the history of the auxilia derives from the Republican era, when the allies of Rome supplied cavalry, missile units, and infantry. These units were transformed under Augustus into a volunteer and professional standing army recruited from the peregrini (the non-citizens) as a supplement to the citizen legions. The roles of auxilia units were quite varied: they still supplied almost all of the army’s cavalry and missile units, and thus played diverse ancillary roles. As the early Empire progressed the auxilia increasingly lost their native characteristics and became standardised in equipment and operations across all frontiers. The final important aspect of the auxilia was that it was a gateway to full citizenship. After twenty-five years of service in the auxilia a man was granted a military diploma which brought full citizenship rights, making service highly desirable.

The only significant forces permanently placed within the Empire were the Praetorian Guard, the Urban Cohorts, and the vigiles – less than ten-thousand soldiers in total, all stationed in Italy. While the Guard’s main duty was to protect and police the imperial palace, Rome, and the surrounding towns, they could also be used in response to internal unrest. For example, Drusus Julius Caesar took two Praetorian cohorts, the Praetorian cavalry, and some of the Batavi guard to deal with a mutiny in Pannonia in 14 CE. At this time the Guard was not large enough to be a significant expeditionary force on its own and would have been supplemented by vexillationes drawn from other units, but they were still clearly able to form part of a mobile reactionary force.

As the only major military power in Italy, the Praetorian Guard continued to extend its influence into the political arena. In 193 they were even able to hold an auction for the right to be emperor. Also in 193, Septimius Severus marched his armies to Italy and defeated the nominee of the Guard, making himself emperor. This demonstrated the key weakness of the early Empire's military strategy: that the soldiers in Italy were too few to defend the emperor or the centre of the Empire. Septimius understood this, and knew that if he had been able to make himself emperor through the might of his armies, then someone else could potentially do the same to him. Therefore he increase the troops in Italy by stationing the II Parthica in Italy and also increasing the size of the escort cavalry. This is one of the great watshed moments of the early imperial army, because it was the first real move towards the military system of the late army.

Septimius did not use the II Parthica in civil war to protect Italy, but it did form the core of an expeditionary army: evidence has been found of its use as far as Syria. The reign of Caracalla (198-217), Septimius’ son, saw the passing of one of the most significant decrees of the Empire which you mentioned in your question, the 212 Constitutio Antoniniana. This conferred the rights of a citizen upon almost all free men and women in the Roman Empire. This had an important effect upon the auxilia. The legal status of men in the legions and auxilia was equivalent. This was a critical step in the on-going standardization of the auxilia, which was becoming an increasingly important element of the army.

The period known as the Crisis/Crises of the Third Century (235-284) was another major turning point in Rome's military system. In the face of snowballing disease, monetary debasement and a breakdown in trade, increasing brigandage, and even climate change, this was the greatest danger the Roman Empire had experienced. In a move of unplanned desparation, the Roman army was forced to change to what has been called ‘elastic defence’. This style of defence was one where the armies were focused on ensuring sovereignty only in their immediate vicinity without any major planning or strategy about projecting force and protecting the entirety of the Empire's border.

The exact details of the period of the Crisis are not entirely clear, and this makes it very perplexing to academics. The field armies of the Empire turned into what was called a comitatus, which was something of a combined administrative and military body that accompanied the emperor. This is, however, something of a contradiction, because a field army could not move quickly if it had the emperor's administration in tow, and nor could it abandon the administrative body to conduct battle or go on campaign becuase this would risk exposing it to undue threats.

This dilemna was solved by the emperors of the Tetrarchy: in 293 a system was created where there were four emperors and each had a capital on a frontier zone. They were able to use their capital as the home of their administration, and the comitatus could easily accompnay them on campaign.

The next major developed happened under Constantine, either in 312 when he fought against Maxentius, or after his defeat of Licinus in 324. Constantine formed an army with two main elements: frontier defenders, called limitanei, and field armies, called comitatenses. The border guards would defend the frontiers against small raiding bands and infiltrators, while the field armies would have the time and distance to respond to major threats. Against the largest threats or during a planned major offensive operation, an emperor could conglomerate multiple field armies into a single large unit. For example, in 377, brought troops from the eastern frontier, including some soldiers from the Saracen people outside the Empire and Roman troops that had been stationed in Armenia, through to Thrace and combined them with the tropps already there. He also requested help from the western emperor, Gratian, who brought troops from Gaul, Italy, and Pannonia to aid Valens in Thrace.

In the late fourth century and into the fifth century, barbarisation was an ongoing process that also affected the Empire's military. Many historians have seen this as coming about as a result of the disastrous defeats and battles that the Roman army faced in the late fourth century, specifically the defeat at Adrianople and the Battle of the Frigidus. Importantly, the difference between many of these new barbarian allies and the allies used during the early Empire, they were now left under their own commanders and in their own field armies. Rather than being divided and incorproated into existing regular Roman army units, and then becoming Romanised themselves, these barbarian allies stayed loyal to their own commanders and own interests, and would just as easily fight against the Empire as for it.

I hope this answered your question! If you have any follow ups, let me know