Clearly we know and understand much about Jesus and his movement in the 1st century CE based on the material/archaeological evidence related to the history and culture of the times, including specific sites and artifacts discovered. However, the existence of any kind of material/archaeological evidence that can specifically be identified with either Jesus or his followers in the earliest period is a controversial one. Most scholars hold that no such evidence exists, however others argue the opposite. As with studies of the Hebrew Bible and Israelites history it seems we have Maximalists, Minimalists, and those in between.
The following is a basic reading list that I am in the process of developing and ever expanding, based on my own research, with both primary and secondary sources, many with hyperlinks. You can click on the link below view the PDF. If you download it you will be able to use the hyperlinks. I will be updating this periodically so check back for a fuller version. Please do not post or circulate. This is for your own study.
The Archaeology of Earliest Christianity: A Preliminary and Expanding Bibliography