Christianity might have become a Jewish sect or a minor religion, but instead it changed the world. Its core believers at the beginning were mostly illiterate. This book by Bart D. Ehrman can be interpreted as a marketing study.
After the death of Jesus, his followers did carry on his mission, but mostly talking to other Jews who were very resistant. The author contends that Paul was a key factor. As a Pharisee Jew he actually had attacked followers of Jesus, but after he "saw the light" he was the first to attempt converting non Jews to the Christian faith without having to adopt Jewish customs. Paul would visit larger population centres and pay his keep with his trade of tent making and talking to whoever would listen. After work he would continue seeking out people to talk to. He would try to get enough believers to establish a church which usually meant meetings in homes. He would move on to another town and repeat the process. Only now he kept in touch with his famous letters.
Paul unlike the original apostles tried to convert non Jews, but had suffered beatings in synagogues and elsewhere. Pagans did not offer life after death and tolerated a variety of Gods. Miracles impressed many converts. One requirement was to reject pagan beliefs and over time this gave the movement more solidarity. Fear of hell (a new concept for most) compelled many to be converted. Christians felt a need to service others and this often included medical assistance. Usually when one household member joined the other members followed. Conversions were slow, but steady and over the first three centuries became significant.
Hardships and torture actually boosted the appeal of Christianity, although not as common as has been pictured. Believers who could endure tortures and barbarities inflicted on them became martyrs in the hearts and minds of pagans. Paganism provided few if any martyrs.
Bart D Ehrman analyses a variety of of scenarios but feels most comfortable with the notion that conversions were mostly in ones and twos, but that over a long time they would have an exponential growth. The greatest success was among the lower classes and more women than men.
Constantine was born a pagan, but was converted before a major battle. He was not baptized until on his death bed, but the author feels it was common enough as they would not have time to sin after the baptism. Constantine did not not try to force Christianity on others, but it was natural that some would convert to gain his favor and others felt it was a natural choice as the new religion was officially approved. He was very involved in the religion, even holding high level meetings to sort out theological disputes. Later Emperors were more aggressive in promoting Christianity.
The author notes that before Christianity became the majority they favored the separation of church and state, but afterwards many advocated Christianity as the state religion. Pagan statues were mutilated. Anti-Semitism was boosted as many Christians thought of Jews as God killers.
The book stops at the fourth century when Christianity had overcome many obstacles. Obviously Christianity has had a major impact on civilization starting in Europe, but as Europeans conquered and colonized much of the rest of the world it grew in strength. There are many historical observations and the author draws on the studies of many other scholars.
For a related perspective on how things beome popular: http://www.therealjohndavidson.com/2018/02/hit-makers.html