To begin, I would like to say that this is an excellent question, as the sixth century is a transformative period in Roman military history. As /u/Shlin28 correctly mentions, our best source for this period is a military manual known as the Strategikon, written by, or on the orders of, the emperor Maurice. I will be drawing heavily on upon it, though it is worth stating from the start that it is difficult to determine how closely the ideals described in it reflected reality.
Before we start, I think it is important to address a few points regarding the terms “Byzantine” and “cataphract.” While there is absolutely nothing wrong with describing the medieval Roman state as Byzantium, in the date you set, 554 A.D., Rome is still organized, politically and militarily, along lines similar with the rest of the Late Antique period. The empire of Justinian bears far greater resemblance to that of Constantine I than of Basil I. One of the reasons Byzantine is such a useful term (when unpacked of previous discarded assumptions) is because the medieval Roman state was quite different (in many respects) than it’s Late Antique predecessor. Therefore, the army of the sixth century bears closer resemblance to that of the fourth century, rather than that of later, more “Byzantine” periods. This is especially true for cavalry. There are several important differences in equipment, organization, and overall tactical role between Byzantine klibanophoroi of Nikephoros II Phokas and those of Justinian. Although there are changes that I will discuss below, in general, Roman cavalry of this period belong to Late Antiquity.
By the time of Justinian, it is evident that cavalry had increased both numerically and doctrinally. Procopius extolls the excellence of Belisarius’s cavalry, and the Stategkion focuses at length on cavalry dispositions. But while the elevated tactical importance of cavalry is clear, the core of Roman armies in this period remained infantry. Numerically, infantry regiments continued to be larger than cavalry, with a paper-strength of around a thousand, compared to around three to five hundred for cavalry. Although cavalry had become especially useful in the “low-intensity” conflicts that characterized Italy and the Balkans, it could never supplant the important tactical role played by infantry in pitched battles, or in rough or heavily wooded terrain. The continued importance of infantry is also borne out in the recorded size of armies. The army sent to North Africa in 533 was comprised of 10,000 infantry and 6,000 cavalry, while that at Busta Gallorum in 552, according to Procopius, had approximately 8,000 infantry and 1,500 cavalry. For a comparison, Julian’s army at Strasbourg in 357 is recorded as having 10,000 infantry and 3,000 cavalry. So while it is clear that cavalry had increased in importance, likely becoming more effective on the battlefield (though I would hesitate to push that point too far), it is clear that infantry continued to play a vital role.
Most cavalry of this period were, to quote Elton, “contact cavalry,” armed with lance and sword to directly engage an enemy. Although the Strategikon places great emphasis on archery, it is clear that not every trooper would have received the rather comprehensive archery training it details, although most were likely equipped with a bow. Aside from being quite the logistical feat, the army employed regiments of light cavalry that specialized in the use of missile weapons. Furthermore, the Strategikon advises that within a regiment of contact cavalry, only those in the middle elements of the file (Late Roman regiments being organized into files eight-ten men deep) should regard the bow as their primary weapon. Like their infantry counterparts, the leading elements of a cavalry regiment (the dekarchs, file leaders; and pentarchs, their seconds) were more comprehensively armored, and wielded primarily a lance and sword. In many regiments, their horses would also have been armored, though the extent to which horse armor was used is unclear. It is these men who would have been expected to do the bulk of hand-to-hand combat, and were thus suitably armored.
For those cavalrymen who did train with the bow, the Strategikon details a rather comprehensive program. Speed was prioritized above aim, and cavalrymen train to loose quickly both mounted and on foot. Cavalrymen could choose to shoot using either the “Persian” or “Roman” manner. The Roman manner appears to have been copied from steppe peoples, and involved drawing the bowstring with the thumb and forefinger. The Persian manner involved using the lower three fingers. Cavalrymen also trained to transition quickly between the bow and lance:
“On horseback at a run he should fire one or two arrows rapidly and put the strung bow in it’s case, if it is wide enough, or in a half-designed case for this purpose, and then he should grab the spear which he has been carrying on his back. With the strung bow in its case, he should grab the spear in his hand, then quickly replace it on his back, and grab the bow.” (Strat 1.1)
As these maneuvers took time to master, the Strategikon also advises constant training, both on the individual and unit level, preferably in friendly territory.
Equipment continued to be largely provided by the state. Aside from the bow, most Roman cavalry would have been equipped with a lance (the Strategikon advises a spare). Bows should be weaker than a man could draw, to prevent him from becoming tired from rapidly shooting. The basic garment of dress remained a loose-fitting long-sleeved tunic in the “Avar” style, though precisely what made the garment “Avar” is unclear. Tunics would have made of linen or wool, and decorated with the patches and roundels that characterized Late Antique military fashion. The Strategikon advises all cavalrymen to wear long hooded mail coats, as well as helmets, a quiver to hold thirty-forty arrows, and a small shield, decorated with the unit’s symbol and/or colors.
Thus, the Roman cavalryman of the sixth century was a highly trained soldier with multiple capabilities on the battlefield. Contact cavalry units were trained to engage the enemy, and wore comprehensive armor and practiced complicated battlefield maneuvers. Likewise, they now possessed missile capabilities, though it should be noted that specialist regiments of missile-armed cavalry were also employed. The cavalryman was viewed as elite (at least in precedence). For the first time in Roman history, cavalry became doctrinally dominant, though infantry remained a vital component of the army.
There is much more about this topic that could be explored, so I tried to keep this as succinct as possible. I’d be happy to answer any follow up questions you may have. I know your post mentioned social background, rations, and pay. For that I’ll need to look into my references at home, so I’d be happy to dig into those later after work.
Frustratingly, I know exactly where to look for the answer, but I have now lost access to my university library and so cannot look at the sources. For what it is worth, a contemporary late sixth-century military treatise, the Strategikon (attributed to the emperor Maurice and probably written by someone in his inner circle), talked a lot about the organisation of the army, particularly the cavalry, whilst Michael Whitby's book chapter, 'Recruitment in Roman Armies from Justinian to Heraclius (ca. 565-615)' in A. Cameron (ed.) The Byzantine and Early Islamic Near East III: States, Resources and Armies (1995), dealt with recruitment in this period. I can talk a bit about the more general aspects of army life, but I suspect /u/HatMaster12 knows far more about this than I do.
Follow-up question.
Would he receive his money monthly? Bi monthly? Or after his service was up?
Another follow-up. What would be a difference in status between the "regulars" and bucellarii?