Liability insurance (Kfz-Haftpflicht) is mandatory. Before registration (Zulassung) your insurer issues an eVB number as electronic proof of cover. Partial cover (Teilkasko) and full cover (Vollkasko) are optional. Request PLZ-based offers first, choose a tariff, then use the eVB at the registration office. Coverage tiers explained: liability vs Teilkasko vs Vollkasko.
Which details you need for a quote and how the PLZ-based comparison works is explained in our guide to the car insurance in Germany calculator. Newly arrived? See car insurance for expats in Germany; if something goes wrong on the road, here is what to do after a car accident in Germany.