From the Roman Kingdom to the Empire, to the Byzantine Period(s). When would the average person be best off in terms of real income?
Follow up, what kind of bundles would a citizen in that time period be purchasing?
This would vary wildly by industry and at different times and in different places, as well as according to individual circumstance. An average-quality pottery-maker with a modest export business in North Africa would probably have been better of in the mid-fourth century CE than in the early first century CE, because his goods would be in higher and broader demand in that period. An Amber Trader would probably see his fortunes rise and fall with the tides of war along the Northern Frontier. A Mediterranean-sailing merchant trader who did business with the Imperial government would probably have made better money under Diocletian's successors than under Augustus' because the late Roman Imperial government paid a pretty penny for reliable shipping. He might not have been allowed to hope that his son would move up the social hierarchy, however, as in the late Empire some trades became heritable by law. An average Roman soldier was probably best off financially and materially in terms of security during the early Third Century, but he might well have envied his late-Republican Era predecessor the piles of plunder that could be won under a great general like Caesar or Pompey, or even his Late-Roman successor under Justinian or Maurice, when pay was still pretty good but discipline was far laxer.
By and large, however, average prosperity probably peaked between the late first and early third centuries CE. The Empire of the time was at its maximum prosperity level. It had not yet fallen prey to the external pressures of an aggressive Persia or the disastrous cycle of invasions and usurpations in the mid-Third century and beyond. Urban society and the safety of long-distance travel and trade were at their height. Inflation was still nominally under control. Elite members of society were still buying into the Imperial system and the urban fabric with their great wealth, moving money around to the enrichment of the masses, instead of sitting on and hoarding their wealth as was more typical in the fourth and fifth centuries. About 1/5th of the population financially subsisted on high amounts of Imperial investment in frontier military communities and in soldier pay, leading to a civilian settlement boom along the frontier (in the vicinity of major forts). Soldiers and their families could expect to have enough money on discharge that they could enjoy a moderately comfortable retirement, or launch successful business enterprises, or they could, and often did re-enlist to keep the money flowing for another 15-20 years. Poor people in major cities could expect to receive a modest level of free food and wine from local authorities, especially at Rome, where imperial largesse regularly took the form of food-supplying festivals and games. The eastern border was largely quiet, allowing for the uninterrupted flow of goods along the major trade routes. The Mediterranean and its hinterlands were experiencing a climate optimum, and producing food (the surplus of which could be sold for profit) at levels far above any period before or since before the modern period. This led to an inflation of overall sustainable population sizes, which in-turn fueled greater economic prosperity.
By the mid-Third century all of this began to change. The climate began to slowly turn less bountiful: desert began to advance in the southern provinces, and colder temperatures slowly deflated the bountiful harvests in northern provinces like Britain, Gaul, and Illyria. Several rounds of plague seriously devastated the increasingly underfed population - smallpox may have made its first appearance at this time. The Germanic peoples of the North achieved a level of regional political consolidation that allowed them to launch large scale, successful raids of the Roman north, and even win a few battles. More resources had to be poured into the Northern frontier, which depressed imperial largesse elsewhere. A largely introspective dynasty in the Persian East was replaced by a much stronger and more militarily aggressive one, and even more resources had to be poured into the Eastern frontier. Inflation exploded the currency system, making soldier pay and coin money inconsistent in value for several generations. The consolidation of Imperial beaurocracy (nessecary to respond to the increased defensive and supply problems) meant that local rich people began to see less and less political-benefit-return on their investment in local civic projects and welfare and spread less and less of their money around, sitting on it and hoarding it on increasingly lavish country estates instead, directly pulling money out of the system and lowering average prosperity as a result. The Emperors of the Fourth Century managed to turn things around a little, and the Eastern Empire in the fifth and sixth centuries before Justinian's Plague experienced a second, more localized prosperity boom, but while the East was booming the West was slowly sliding into terminal economic decline.
After Justinian's Plague, the Eastern Mediterranean region would not see another such a collective prosperity boom until the rise of the Ottoman Empire in the 15th Century, and the wider Mediterranean would not see one until the modern era.