What should we expect to find about Jesus

Coming from centuries of Christian culture, we assume that Jesus of Nazareth must have been well documented by both the Jewish and the Roman authorities. I think that we should instead look at the documentation for other figures of the time, and base our expectations on what we see in other cases.

There are four Jewish leaders whom I think present a sufficient parallel or might even have had a greater importance for the Romans. These are
Hillel, who died about the time Jesus would have turned 10,
Yokhanan ben Zakkai, who approached the Romans for permission to start the Jewish academy at Jamnia after the destruction of Jerusalem
Aqiba, who was a major spiritual leader at the time of the Bar Kokhba revolt,
and Simon bar Kokhba, who lead a rebellion against Rome in the early 2nd century.
The question I will pursue regarding these men is what sources we have for their history.