Recently I've gotten quite interested in the Germanic peoples during the Classical Antiquity, particularly their general lifestyle, social hierarchy and their relations with the Greek city-states and Roman republic and empire. What are some reliable books I could read for more information on the topic? Thanks in advance.
You didn’t specifically state a desire for information about Germanic martial culture but it is an important piece of the puzzle given their religious beliefs and general pervasive proclivities for violence.
I would suggest the Routledge press volume titled “Ancient Germanic Warriors: Warrior Styles from Trajan’s Column to Icelandic Sagas” by Michael P. Speidel Ph. D.
I think the best introduction would be Heather's "Empires and Barbarians" which generally covers from the 1st Century BC all the way until the 10th Century AD.
However, Heather is one school of thought. There are others, although most focus specifically on late antiquity, while you're asking for earlier.