Faithful Jews born and raised in Temple and synagogue worship, were to go out and "be the church" that Jesus said the very gates of Hell would not prevail against. The church they built was based on the patterns of worship that were given to Moses from God. According to Acts they attended Temple and the synagogue observing the daily liturgical prayers they were raised with. They attended Sabbath services and kept it holy, but on Sunday they went to one of the faithful's homes to celebrate the Lord's Supper or Eucharist as commanded by Jesus. This cycle they repeated every week, until right around the time of Acts 7 with the stoning of St. Stephen. At this time, and surely before, it had become quiet clear that this transformed understanding of Judaism was not welcome. By Acts 21 it had reached the point that Paul was not welcome in the Temple and a mob attacked him. These persecutions forced Christians out of the Temple and resulted in a distinct form of Judaism, a "Christological Synagogue", that would be called Christianity or the Way.
When the Scripture refer to a "house church" it is something very different than the 20th century notion of people hanging out on couches, playing guitar, eating munchies, and having a bible study. When Christians gathered in a house they were forming a synagogue. In fact James, when writing to "the twelve tribes scattered abroad", called their gathering in James 2:2 just that-a synagogue. They gathered to perform the liturgical services they learned in the synagogues in which they were no longer welcome. They did not abandon the synagogue, the synagogue abandoned them. Like the synagogues of old, they started in homes and over time were able to build what we would recognize as churches. But in the mean time, they worshiped in houses. From archeological evidence we are able to learn that "house" might not always be the right word. Mansions would be better. They were locations that were big enough to hold a large congregation and some of these house churches had baptismal fonts built into their structure.
Added to the core synagogue structure (called the Liturgy of the Word), was the transformed and fulfilled Temple worship, the Eucharist, which was inserted prior to the benediction. At this "Christological Synagogue" the Bishop would be seated on the bema. The ark would go from containing the Torah to enthroning the Gospel narratives which would be proclaimed from the bema. After the prayers and Scripture readings, the Liturgy of the Eucharist would be celebrated. This image of worship is what Paul has in mind in Colossians 3:16, "Let the message of Christ dwell among you richly as you teach and admonish one another with all wisdom through psalms, hymns, and songs from the Spirit, singing to God with gratitude in your hearts."
By the time we get to Acts 15, the Church in Jerusalem had quickly become the "Mother Church" for the early Christians. We learn that James is the leader (Bishop) of the church, and when a issue arises that affects all the other churches, it is brought before this church to make a ruling. After the ruling was received, a letter was sent to the other churches with the expectation that it would be obeyed (Acts 15:30). It is clear that even during the time of Acts, a structure of church authority was well established. The 20th century notion of someone just starting up their own church without being in connection with the "mother church" would have been viewed as clear heresy.
This Christological form of synagogue worship was taken with Paul and the rest of the Apsotles as they went on his missionary journeys. Those newly forming churches, both Jewish and Gentile, adopted both the pattern of worship and the structure of authority exemplified by the Jerusalem Church with universal acceptance.
From what we know about the life of early Christians, their worship was not spontaneous and they did not decide by themselves how they would worship. Rather it was based on the patterns of worship given by God of what Heavenly worship is like. There was and is a foundation of order and structure as we are encouraged to do in 1 Corinthians 14:40, "Let all things be done decently and in order." There also was and is a hierarchy of church authority which we are required to be submissive to, as in Hebrews 13:17, "Obey those who rule over you, and be submissive, for they watch out for your souls, as those who must give account".
These patterns of heavenly worship in both structure and authority are still to be found in Orthodox churches worldwide. You can walk into any Orthodox church or monastery and see parishioners living out this Heavenly worship. From the time Christ said it, until the present, the gates of Hell have not prevailed against it. The church of Acts 29 is still here, alive and well.
After attending a Divine Liturgy in the Hagia Sophia Catherdral in Constantinople, envoys of Prince Vladimir of Russia gave this report:
We knew not whether we were in heaven or on earth, for surely there is no such splendor or beauty anywhere on earth. We cannot describe it to you; only this we know, that God dwells there among humans, and that their service surpasses the worship of all other places. For we cannot forget that beauty.
Find the time to visit an Orthodox church and see it for yourself.