Help choosing a "home base" while in Germany

Nurnberg. Great town, close to most anything in Bavaria, easy train ride to Prague.

Why were you thinking those three, specifically? They sound very different from each other, possibly a bit arbitrary

I agree that Nuremberg is generally a great base town, logistically speaking, for outings and variety of experience... but what's good for you depends on what sort of place you want to stay in, and what places you want to visit - and what you wish to do and see too.

I like Boppard in the Middle Rhine Valley (a UN ESCO World Heritage site) as well. More people than Rothenburg but not so many danged tourists, and not half a million residents like Nuremberg - and it's in a place of real natural beauty, not far from places of historical interest, both big and small.

https://www.youtube.com/watch?v=J2IjTma6VRY

Rothenburg ob der Tauber is bad for day trips as the train connections are poor. Würzburg (my favorite) or Nürnberg would be better.

Frankfurt am Main is a major train hub and would have great connections. However, late March might still be in Messe season when major trade fairs are held. The rooms fill up and cost vastly more. Check HRS.Com or another booking site to see what might be available .

I found Heidelberg a bit expensive and the train station is not close to local sites. We enjoyed a visit there a couple years ago but we would not want to use it as a home base. That might just be out lack of exposure to it.

I would not recommend any of those cities as a base.

Heidelberg is great, but expensive. Still, it deserves a visit.

My favorite areas of Germany are Bavaria and the Rhineland. I suggest flying in to Frankfurt and heading down to Heidelberg for a day, then move east to Wurzburg, where you pickup the Romantic Road.
https://www.tripadvisor.com/SmartDeals-g4586437-zft9624-Romantic_Road-Hotel-Deals.html#MAPVIEW
https://www.romanticroadgermany.com

There is much to see on the road. Rothenberg on the Tauber is the highlight, but places like Dinkelsbuhel are also intact medieval walled cities, without all the tourists. The road starts in Wurzburg and ends in Garmish/Fussen.

After doing the road, Munich is a great place to base, going from there to Salzburg, Austria and Berchtesgaden, Germany. Also, Nuremberg.

I trust you understand that you don't have all of Germany at your feet, after selecting any "home base". You have to select an area where you want to explore. It sounds like you may be covering a vast amount of territory, so I hope you have allocated enough days on the ground. In particular, I think it's not ideal to start in London if you want to cover a lot of Europe. For example, your OP doesn't mention any of the places Eurostar sells direct tickets to.

Choice of a home base in Germany depends a lot on what you like to see. And in March, mountains and gardens are less desirable. So I might suggest an urban destination, like Cologne, Dresden, or Berlin, since the latter two have good access to Prague. Berlin is good for a week, even with only S-Bahn excursions.

Tim's right about selecting an area to explore. But you are likely asking, "what's an area?" Well, "Bavaria" is an area, but it's a gigantic one for which a single base town just won't work. geovagriffith seems to have Bavaria broken into two parts - one north, one south. He has added another vote for Nuremberg in the north. Then in the south, he offers up Munich as a base, for Salzburg and Berchtesgaden... but even southern Bavaria is still pretty big, and for some of us, day trips like these, though they're almost entirely in southern Bavaria, still require way too much ground travel. YOU need to do some homework on your own to find out whether a certain base town works for the places you wish to visit. A Munich - B'gaden - Munich day trip will mean at least 5 hours on the train in one day. A day trip to Salzburg is shorter - like 3.5 - 4 hours. Are these travel times doable? Depends. Salzburg for example may be the sort of city you need to spend a FULL day in - it just depends on what you want to see there.

If you are deciding which of the three listed above, then I vote for Frankfurt for all the obvious reasons.

If you aren't too concerned with the weather, ie the cold, etc, then I would suggest as "home bases" Hamburg, Berlin, Leipzig for several reasons. It's best to be on one of the trunk lines.