Check24 is a German comparison website, that compares prices for different companies across many different fields. As car rental costs can vary so widely, we recommend checking here first before deciding on a company to rent a car.
Renting a car can be a great option for the most travel flexibility in Germany. When you first move to Germany, you will be able to use a driver's license from another country, but if staying long term, you should trade in your license for a German one. The procedures for changing your license vary from country to country, but this is where you'll have to go to switch your license in Berlin: https://service.berlin.de/standort/121646/