How were early Christians viewed by non-Christian Roman authors and why? How can I start a research paper on this topic?

Your starting point in your essay should be to mention that from the Roman point of view, early Christianity was simply a minor offshoot of Judaism. It was not particularly important and thus gets very little attention. Christianity tended to be regarded as a rather secretive and fanatical cult, and garbled descriptions of the Eucharist led some Romans to consider them cannibals. The main concern was that because they refused to offer even a single pinch of incense to the imperial cult, they were possible rebels or traitors, something of far greater concern in the religiously diverse Roman Empire than their theology. The main sources are:
Josephus' Antiquities of the Jews, (93–94 AD): This discusses Jesus as a teacher and miracle worker who was crucified by Pontius Pilate.
Tacitus's Annals (116 AD) refer to "Christus" being killed by Pontius Pilate. He sees the Christians as one of many cults and superstitions that arose in the period and argues that persecution caused the religion to spread.
Lucian of Samosata (c. 115–200 C.E.) writes about Christianity satirically in The Passing of Peregrinus. The work satirizes credulity and superstition in general. The most distinct feature of Christianity he mentions is that because Christians believe themselves immortal, they seem almost actively to seek out death.
Pliny (112 AD letter to Trajan): In his correspondence with Trajan, Pliny is concerned about how to treat Christians brought before him for breaking the law. He describes them as stubborn but basically harmless and is mainly concerned with balancing mercy with a need to discourage rebellion.
Suetonius (c. AD 69 – c. AD 122) in Lives of the Twelve Caesars has two sentences which seem to indicate that he thought someone named Chrestus was associated with a group of rebellious Jews. 
https://www.biblicalarchaeology.org/daily/people-cultures-in-the-bible/jesus-historical-jesus/did-jesus-exist/