We have very little information about most of the Judeans of that period, because many of them were not literate. Our sources for this are mostly the historian Josephus (who is hard to trust especially on this particular question, because he was writing for the Roman emperor), and Jewish rabbinic literature of the first and second centuries.

In that body of literature, Rome is mentioned a fair amount, with different valences in different places. For example, in one story, several rabbis get into a debate, in which one says that they should be grateful to Rome for building roads and aqueducts and bathhouses, and another says that the Romans did those things only for their own gain and/or for idolatry, so Jews shouldn't celebrate them. There are also a number of stories in which important rabbis have conversations or debates with Roman officials, in which the Romans often come off as not especially intelligent, and pretty dangerous, but not totally evil.

There are also a large number of martyr narratives, in which Jews are killed horribly by the Romans, but most of them from are after the Bar Kochba Revolt in 135 CE, so they don't tell us much about the first century.