Brad Argent and The Genealogy Guy explore the connection between genealogy and DNA research in shaping one's identity. They highlighted the significance of understanding one's ancestry and genetic makeup to gain a sense of identity and discuss the transformative nature of DNA research in providing a tangible connection to the past and one's ancestors. They also emphasized the importance of capturing family history through audio recordings, conducting thorough historical research and verification, and leveraging local newspapers in genealogical research.