Well according to Hitler's Tabletalk, Hitler intended for his successors to also bear the title of Fuehrer (he intended for the Fuehrer to remain as a sort of Pope to the German people, standing above the law and representing the future and will of the German volk). The Fuehrer was supposed to be elected by a Senate (in his speech on the decision to wage war against Poland on 1 September 1939, Hitler implied the creation of such a body, stating that should he (Hitler) die, then Goering would be his successor, if Goering died, Hess would be the next Fuehrer and if Hess died, then the Senate would convene and elect a new leader, although at that time such a body did not exist).
The holders of key offices in the Party would be members of the Senate and understandably the elections would take place behind closed doors, similar to the way the Cardinals elect the Pope. The Reichstag was supposed to be retained, though one can assume that it would still have no power, and the one elected by the Senate would become the next Fuehrer.
However, it is quite possible that, in an interregnum after Hitler's death (he would probably have died in the late forties or early fifties, given that he suffered from Parkinson since 1932), the various positions might have been separated. They might have briefly ended up with a Politburo-style collective leadership (one could imagine that Bormann heads the party bureaucracy and controls the Gauleiters as a sort of general secretary (a position he de facto held as head of the Party Chancellery), Goering becomes Head of State as Reich President or Reichsverweser (Reichsverweser is German for Regent), with Himmler and Goebbels also in important positions, with some important Gauleiters (Kaufmann, Hanke, Griesler) and SS leaders (Wolff, Heydrich, Best, Kammler) thrown in for good measure.
I do not think that the Wehrmacht would be able to seize power. It was divided and weakened by infighting between the services (especially between the Navy and the Luftwaffe). Manstein, Rundstedt and Guderian were, undoubtedly, competent generals, but that does not immediately mean political accumen. And even if one general thinks that he wants to start a putsch, his regiments might follow, but that does not mean that the others will as well.
If Hitler had died somewhere between 1935 and 1940, then his successor would have undoubtedly been Goering. Then Goering had everything working to his advatange -- he was an old comrade, but not a plebeian like Goebbels, he was very popular among the German people, seen generally as a "moderate Nazi" by the rest of the world, was acceptable to the Wehrmacht since he had little contact with the Party apparatus. However, as the war goes on Goering's powers waned (he was already in decline in 1939, because he arranged the Munich conference behind Hitler's back and was opposed to the decision of invading Poland because he feared it could lead to a war the Reich would lose), and, especially in the critical years 1943-1945, the powers of Himmler and Bormann increased.
Himmler could have become Hitler's successor. It would surely be a very bizarre regime. After all, Himmler wanted the SS to become the new nobility of the Greater Reich and rule it is as the new military-religious order, similar to how the Teutonic Knights had their own state in Prussia. Thus he allegedly intended to re-create the State of Burgundy, with Léon Degrelle as chancellor, subordinate to a Reichsverweser, who was supposed to be the Reichsfuehrer of the SS. But Himmler, pragmatic as he was, might very well have made a brief alliance with national-conservative elements in Germany, such as Goerdeler. After all, in August 1943 he and his Chief of Staff Wolff met a few times with emissaries from the "German Resistance". After all, Himmler would have had to weaken the influence of the party bureaucracy, which was loyal to Bormann.
In any case if Himmler becomes the new leader, either openly as the second Fuehrer or as the Grey Eminence of a coalition government, one can expect the SS coming to control the Reich even more (already during the war, the SS was a state within the state, with hundreds of SS-controlled corporations, and a good deal of SS members assumed political posts ( SS-Obergruppenfuehrer Dr. Werner Best became the Reichs Plenipotentiary in Denmark, SS-Brigadefuehrer Professor Dr. Franz Alfred Six worked in the Foreign Office in the Cultural Department and was supposed to be involved in training the new generation of diplomats, SS-Gruppenfuehrer Dr. Stuckart was State Secretary in the Interior Ministry, SS-Gruppenfuehrer Otto Ohlendorf was Undersecretary of State in the Economics Ministry etc.).
Bormann could also have become Hitler's successor. But no one in the public knew Bormann and he had absolutely no charisma, nor any desire to be known as the people's tribune. So he would probably have appointed some puppet President and puppet chancellor (according to Jochen von Lang, who wrote a very good Bormann biography, Grand Admiral Doenitz, if the Political Testament of Hitler had been fulfilleable, would have become a puppet of Bormann, who was named in the Testament as Party Minister, because he lacked experience in statecraft, while Bormann was a canny intriguer), and ruled behind the throne through his control over the Party administration, which would have led to an increase of power of the Gauleiters, who were, after all, an important source of support for Bormann. But naturally he would have had to purge the SS and the Gauleiters of disloyal elements. It would have been a highly bureacratised Reich, somewhat similar to the USSR. And given Bormann's anticlerical and anti-Christian leanings, one can expect a campaign against the Church.
Of course, after the old guard is dead, then it is an entirely new deck of cards. Then we have the next generation of Gauleiters and SS commanders (given that the Gauleiters became little princes in their fiefdoms and the SS gained a lot of influence in the conquered territories, one could expect that in time the government in Berlin would have had little control over the Reich).