Just want to point out, Matthew collected taxes in Capernaum. Hence he was collecting taxes for Herod Antipas, not Rome. Capernaum fell within his tetrachy, and Rome generally subsidised levant client states to act as buffers against her enemies or to keep the peace, not as sources of income. So the taxes Matthew collected would have gone into Antipas' treasury and likely used to build his cities like Tiberias.
Matthew was a Publicanus. We translate this as tax collector, but it was more a public contractor. Publicani bid on contracts for the state, be it building projects or maintenance or tax farming. The latter was the most visible activity they undertook, and hence people started seeing them only in that light. No one likes the taxman, but the state needs money to maintain infrastructure and defend itself.
Tax farming entailed bidding on the presumed taxes an area is supposed to bring in. The tax farmer then supplies that amount to the state, and attempts to recoup it by collecting the taxes owed. Anything he collects above the bid that the state had accepted, is profit to the tax farmer for his trouble. This gives the state a steady income in good or bad years, where the risk is taken by the tax farmer that the district won't cover the amount, and he runs a loss, in bad years. In good years, the tax farmer can make a tidy profit, so often became quite rich in prosperous times. It is also a system very prone to abuse by the tax collector himself, as he has a personal interest in squeesing every red cent from those in his district, while the state still gets the same amount each year. Taxes were reassessed on a regular basis, usually about every 15 years (the Indiction), depending on province.
So Matthew perhaps had other state contracts as a Publicanus, and certainly was disliked for collecting taxes - a known abusive and corrupt occupation. This was for a Jewish client-king of Rome though, not Rome directly.
It also means he was fairly educated, at least middle class, probably conversant in both Greek and Aramaic, and certainly literate. There is a tradition derived from Papias that he wrote his gospel in Aramaic, hence groups such as the Judaising Nazerenes claimed to possess the original. Alternately, some supporters of the Peshitta says it has the original version. I have even seen argued that the theoretical Q gospel is Matthew's Aramaic gospel. The current Gospel of Matthew was certainly likely written in Greek, so is probably not a translation thereof, and has been ascribed to Matthew since the 2nd century. Church tradition suggests he wrote both a Greek and an Aramaic gospel therefore, which is certainly possible based on his background.
There is also debate if Levi and Matthew are the same person, as Clement seemed to have listed them separately, but in general the Church seemed to have conflated the two since very early times.
