As they did with every other aspect of life, so did the Nazis establish a government agency to control the musical life of the country as soon as they gained power. It was called the Reichsmusikkammer (Reich Music Chamber) and everybody involved in the music business was required to become a member; and conversely, the RMK could refuse membership to anyone it wanted, thus effectively barring them from performing or publishing music. Needless to say, only "Aryans" were allowed to join.

Goebbels was the ultimate head of the RMK. As Minister of Propaganda he was also the head of the ReichsKulturKammer of which the RMK was a part. All forms of artistic expression were harnessed to the Nazi cause and Goebbels was particularly interested in the power of music (and film) to speak directly to the emotions of the people. He commissioned all kinds of stirring marches and patriotic songs celebrating the Führer, the Volk and the Vaterland.

However, it wasn't all marches and Horst-Wessel-Lied. A substantial number of light-hearted musicals were filmed, for example, to provide the audience with much needed distraction and entertainment. They sometimes bore a marked resemblance to Hollywood musical extravaganzas, an example being Es leuchten die Sterne (1938), a medley of which can be seen here. Very popular were the Zarah Leander movies with her trademark melancholy and moody songs, which struck a chord particularly as the war dragged on, such as Ich weiß, es wird einmal ein Wunder gescheh'n ("I know that one day a miracle will happen") in 1942.

But the best way to answer your question would be to look at Wunschkonzert (1940), a film about an immensely popular radio request show for soldiers. The titular request show features the following eight pieces:

• Paul Hörbiger (he later starred in The Third Man) with Apoloner, Apoloner bist Du about which I can't find any further information

• Comedian Weiß Ferdl sings Bin ich froh, ich bin kein Intellektueller which goes “I am so happy that I am not an intellectual, not a know-it-all, not very smart at all. It's often come in handy, a little stupidity goes a long way...”

• Hans Brausewetter, Heinz Rühmann, Josef Sieber sing the jolly singalong Das kann doch einen Seemann nicht erschüttern (Nothing can shake a sailor) from the 1939 film Paradies der Junggesellen (Bachelor's Paradise)

• Wilhelm Strienz' tearjerker Gute Nacht Mutter (Goodnight, mother).

• The extremely popular singer Marika Rökk with the crowd pleaser In einer Nacht im Mai from the 1938 film Eine Nacht im Mai (One Night in May).

• A group of soldiers singing the war song Soldaten sind Soldaten (Soldiers are soldiers) which I am not linking to as it seems to be uploaded exclusively by neo-nazis.

• A clarinet solo.

• The Philharmonic Orchestra of Berlin playing the overture to Mozart's Figaro.

So there you have it. As this was the second highest grossing wartime film in Germany, we can safely say that this is a cross-section of what music was popular at the time.

I wrote my B.A. thesis on the role of Beethoven in the Third Reich and, while not answering your question, want to add that it's way more complicated in his case than talking about a "fascination". In short, Hitler didn't really like Beethoven, at least that's what we know through sparse sources on the matter. Also, Beethoven's heritage and familiar background didn't really fit into the Aryan Mastermind narrative. Even more than that, he wrote the music to Schiller's Ode "To Joy" with its key line being Alle Menschen werden Brüder (All men become brothers), which was exactly the opposite of the fascist ideology.

The problem was: Beethoven was really, really popular. They couldn't just fade him out of the musical programme, so they played along, but you can see a steady decrease in the amount of Beethoven recitals in the Third Reich over the years.

To sum it up, and I hope it's not too far off topic for the mods: Beethoven wasn't a Wagner and would've never been one for the Nazis.