The first and most important document you'll get proving your German citizenship is your Staatsangerorigkeitsausweis - or citizenship certificate. It's not, however, a valid piece of ID. But you will need this to apply for your German ID card - or Personalausweis, as well as your Reisepass - or passport (more on these below).
When your citizenship application is successful, your local authority should automatically register your new German nationality - meaning you should be registered to vote right away in German federal and state elections. If you're not sure whether your local authority registered you properly though, you can always book a registration - or Anmeldung - appointment and bring your citizenship certificate with you. Obviously once the Burgeramt has you registered as German, you no longer need a residence permit. So if you have any appointments at immigration offices coming up, you can go ahead and cancel them.
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