The only history I've read about this time frame is Michael Grant's very good, but out-of-print, book The Twelve Caesars
My strongest impression was that Caligula came across as far more reasonable and capable than his depiction in I, Claudius
. Propaganda spread by his adversaries has dominated the popular impression of him. In contrast, Tiberius was presented more harshly by Grant.
Also, very little is known about Livia, and Graves must have made up most of the narrative about her (though the family tree is completely accurate).