The German Alps + towns + sights are not just a day trip from Munich. I would spend the 2-3 nights that you appear to have available closer to or in the mountains.
"I'm looking for the classic scenic Alps theme."
These are not the Alps of the Switzerland, so if you're thinking Bernese Oberland with Jungfraujoch, or the Matterhorn and Zermatt, you need to adjust your expectations somewhat.
"Salzburg was suggested also as a home base. For Berchtesgaden > Neuschwanstein"
Well, lots of people make plans to visit Salzburg and Munich for other reasons than then Alps - then squeeze in their Alps visit on day trips from these places. And then they recommend doing what they did. Salzburg is surely closer and a better base than Munich - and it can be an OK base for getting into the mountains briefly on one day. But it's still a vastly different kind of experience if you stay in one of these cities instead of in the mountains. If your goal is to "feel" the Alps of Bavaria, then you should stay among them somewhere.
No savvy traveler would ever suggest Salzburg as a base for visiting Neuschwanstein. Way too far.
But then Neuschwanstein - not a real castle, but a late 19th-century mock-up with a fake castle exterior, with an overpriced and overcrowded 30-min. tour - is nothing I would build an itinerary around anyway. There are many other more significant and more interesting/fun places and things to see and do in both the Füssen/Garmisch and the Salzburg/Berchtesgaden regions.