I admit I haven't read this entire thread, but I wonder if anyone has brought up the Indo-European culture as a whole yet.
If you REALLY want to trace German roots back, look at the language. German is an Indo-European language, just like the Celtic languages, Romance languages, Slavic languages, and Persian and Indian languages (Persian, Urdu, Sanskrit, Punjabi, etc.).
So this tells you something: all of the people who speak Indo-European languages have some kind of common historical and cultural background, even if it has become very diversified over the millenia since then.
It all goes back to the early Indo-European civilizations, and this seems to center around the people who were in the Bible called the Hittites. They lived around northeastern Turkey, around the Caucasus Mountains. The Goths and Celts would later return to Turkey and set up cities like Galatia (named after the Gauls), though this part of the world usually isn't associated with Germanic or Celtic cultures. The Hittites seem to have been a largely tall and white population, and possibly very war-like. In the biblical story where David has an affair with the wife of one of his military officers while that officer was leading a war, the military officer was a Hittite leading the Hebrews.
Long story short, some other civilizations got together and annihilated the Hittite civilization in Turkey some time around 1500 BC. After this, the Hittite people made a mass exodus, seemingly in all directions. Primarily they migrated across northern Europe (where they became known as Celts and Goths), west across the Mediterranean (where they were known as Trojans, Etruscans, Greeks, and later became Romans), and to the southeast to modern-day India, where they were called the Aryans.