More 'objective' records on the early Christian community
Time for some scholarly expertise:
My syllabus of 'History of Rome', pp. 181-185 concerns testimonies of non-Christians who witnessed the gradual growth and success of Christianity.
The earliest external testimonies come from Tacitus, Pliny the Younger, Suetonius, and the "Testimonium Flavianum" (ascribed to Flavius Iosephus).
Tacitus (Annals XV, 44) speaks of the fire in Rome in 64 AD: emperor Nero, suspected of having started the inferno himself, puts a people called 'Chrestiani' to blame for the disaster. Some of them are found guilty, not on the charge of arson, but of 'hate against humanity' (odium humani generis). Some are to be schredded by dogs, some stabbed onto burning crucifixes, lit like candles. Emperor Nero was kind enough to offer the space of his own private gardens to display the crucifixions. Tacitus holds no sympathy for their religion, which he characterizes as 'pernicious superstition' (exitiabilis superstitio). However, he feels sorry for them and believes they deserve mercy, because their deaths does not serve public interest but just the cruelty of a single man.
In his 'Life of Nero' (Vita Neronis, 14), Suetonius alludes to the same events, though without mentioning the fire. He writes that, under Nero's administration, correctional actions are taken against Christians in the sense that they're punished by death. He describes them as a bunch of people that have surrendered themselves to a new and dangerous superstition (superstitio nova ac malefica).
About 110 AD, Pliny the Younger is governor of Bithynia and asks his emperor Traianus instructions on how to treat the Christians. Traianus responds that he does not have to hunt them down. When they are reported or charged of a crime, Pliny must put them to justice, unless they're prepared to offer 'to our gods'. Pliny is ordered to disregard anonymous charges, because this gives a bad example and doesn't respond to the spirit of their aera (nec nostri saeculi est, Plinius Minor, Epistulae X, 97).
Finally, there's the famous 'Testimonium Flavianum', a passus in the 'Antiquitates Iudaicae' (XVIII, 63-64) presumably by the hand of Flavius Iosephus. In this work, published around 93-94 AD, the author acclaims that Jesus Christ did miracles, had a high appeal towards Jews and Greeks, and appeared alive before his pupils on the third day after his death. This passus is considered to be a complete or at least partial interpolation inserted later on, dated approximately 300 AD.
If you're interested, my syllabus proceeds with the prosecutions of the Christians, which was a very gradual but mainly unplanned project in the eyes of the Romans. Notably, the most important evolutions in this complex scheme can be found under the emperors Domitian (81-96 AD), Hadrian (117-138 AD), Tertullian (see his 'Apologia' about 200 AD), Decius (249-251 AD), Valerian (253-260 AD), Diocletian (284-305 AD) and his 'Caesar' (co-emperor) Galerius.
You should all never forget that the Bible (itself being a 'compilated' work of several texts) is in the first place a work of a religious community that wanted to transfer the message of Revelation, salvation, forgiveness (mostly through the Gospels) and primarily appeals to human moral and beliefs.