Actually, Karl Dönitz was appointed President, Reichspräsident, and Joseph Goebbels became the Head of Government (Reichskansler). The day after Hitler´s death Goebbels killed his six children, went out to the garden with his wife where she took poison and he shot himself. This meant that Dönitz was the only head of state. After the war Dönitz was sentenced to ten years in prison after which he moved to Auhmühle in Schleswig-Holstein where he wrote his memoirs and lived on a captains pension (the rank he had before Hitler promoted him). Dönitz died in a heartattack in the early 80´s.
Göring was dismissed from any of his numerous positions, because being in the Alps instead of fighting an Endkampf in Berlin in April 1945, he sent a telegraphic ultimatum to Berlin. It's content was that he would resume the entire Leadership of the Reich, if he wouldn't get a telegraphic response from Hitler in a certain time. That silence would mean the "Führer" "wouldn't be able to act at all". Thus Göring could try more openly to get a cease fire arrangement with the Western Allies. (Well the man was a known drug addict).
This telegram did enrage Hitler so much that he ordered to totally dismiss Göring and have him arrested by the SS. And he ordered Dönitz who was in Kiel/Flensburg then, to become the next head of state. He chose Dönitz, who lost one or two sons being U-Boot Kapitäne in WW2, simply because he was one of the most fanatical Nazis in the high Command. Goebbels on the other hand, who as a more left winged Nazi and fanatic contemplated an arrangement with the Soviet-Union against the Wallis, stayed faithfully to his master in Berlin for the Götterdämmerung. Thus not being an obvious choice for the leadership.
Oh, and in spring 1945 Hitler ordered preperations for destroying the entire German economy. Because: In the titanic racial struggle the German people is weaker than its enemies. Thus it will perish and doesn't need any economy no more. After the war Speer stated that he sabotaged this "Nero" order, which isn't entirely true.