Keep a calendar showing where you physically worked each day. Distinguish the German workplace, your home abroad, business travel and leave. Save tickets only where they may support an expense or travel record relevant to your situation.
Create one folder for the signed contract, addenda, payslips, insurance correspondence and authority letters. Record whom you contacted and when. If payroll treats your circumstances differently from what you expected, ask for an explanation promptly rather than waiting until year-end.
Good records do not decide legal treatment, but they let an employer, insurer or adviser work from evidence instead of estimates.