Allow me to share a couple of more short passages from a writer, Alfred Edersheim, who was considered an expert witness in this matter. From Chapters 17 and 18 of his Sketches of Jewish Social Life.
Of course, the synagogue system is not in every way to be equated with the church.
As a rule, synagogues were built at the expense of the congregation, though perhaps assisted by richer neighbours. Sometimes, as we know, they were erected at the cost of private individuals, which was supposed to involve special merit. In other cases, more particularly when the number of Jews was small, a large room in a private house was set apart for the purpose. This also passed into the early Church, as we gather from Acts 2:46, 5:42. Accordingly we understand the apostolic expression, "Church in the house" (Rom 16:3,5; 1 Cor 16:19; Col 4:15; Phile 2), as implying that in all these and other instances a room in a private house had been set apart, in which the Christians regularly assembled for their worship. Synagogues were consecrated by prayer, although, even thus, the ceremony was not deemed completed till after the ordinary prayers had been offered by some one, though it were a passing stranger. Rules of decorum, analogous to those enforced in the Temple, were enjoined on those who attended the synagogue. Decency and cleanliness in dress, quietness and reverence in demeanour, are prescribed with almost wearisome details and distinctions. Money collections were only to be made for the poor or for the redemption of captives.
It was customary to have service in the synagogues, not only on Sabbaths and feast-days, but also on the second and fifth days of the week (Monday and Thursday), when the country-people came to market, and when the local Sanhedrim also sat for the adjudication of minor causes. At such week-day services only three persons were called up to read in the law; on new moon's day and on the intermediate days of a festive week, four; on festive days - when a section from the prophets was also read - five; and on the day of atonement, six. Even a minor was allowed to read, and, if qualified, to act as translator from the Hebrew to the Aramaic.
Takeaway: There were no money collections to pay the "Staff" or the rulers or the chief rulers of the synagogues. Yes, there appear to have been chief rulers of some sort. Note the word only in the first quotation.
Even children could participate in the formal readings. I find this last point interesting in view of the previous discussions from years ago on the various house church forums. It was regularly asserted that the scriptures had little usefulness in the early church because that vast majority of Christians were illiterate.