Germany under Goring would see the same racial policies as OTL Germany saw (Nuremberg Laws, plus all the other legislation limiting different races rights) since Goring was among those who signed those laws in the first place. I doubt he would back out. Him being a "moderate", or "moderate for a Nazi" is kind of an overstatement, based on the fact that he was among those in the top leadership that wasn't itching for war. And that was it, he was down with everything else that happened in the Reich, there are literally tons of paperwork proving that leftover from the Nuremberg Trials. So Goring probably wouldn't start a war - he was too into living a comfortable life and basking in the prestige of being a leader to put such a burden onto himself.
He does have a good shot at becoming leader. The idea that Himmler would take over is idiotic - the SS only became something of a force to be reckoned with during the war, and even then was always dwarfed by the Wehrmacht. It is more likely that Himmler would be dismissed by Goring once he became chancellor and Himmler's career would end there. Goring's real competition would be Rudolf Hess who was the chief of the party. It is important to remember that Nazi Germany officialy did not have a Deputy Chancellor - if Hitler died, a new one would have to be elected. Hess is at the head of the Party after Hitler so he has a good chance of getting the votes; OTOH Goring is the President of the Reichstag and Chief of the Luftwaffe with some support in the Army. He does stand a good chance at pulling off a night of long knives using the army, and maybe the police through his ally Frick.
And later? I wouldn't paint him as a joke who spends time high on morphine eating doughnuts. He was able to be somewhat competent during the Nuremberg Trials, if he had to rule a country where a lot of peoplewould probably wan't to usurp him, he would more likely keep his guard up than ignore the threats. He would still inherit all the problems Nazi Germany had before the war, and given his performance as the chief of the 4 year plan office, things might go both ways: he did make a lot of bad stuff happen to the economy, but didn't go all the way as many wanted him to (such as full nationalization of all industries, which would have been a nightmare). Hard to say if that was him learning from mistakes, being able to listen to advisors or dumb luck combined with incompetence at doingwhat he was ordered to do. He would be a ruler of a totalitarian state. This would give him a lot of options at "fixing" German problems, even if it meant killing Germans.