When I was getting into it a few years ago, I read Germany: Memories of a Nation by Neil MacGregor. I loved it and its a very accessible work.

It originated from a BBC Radio series by a historian, which I never listened to, but searching it up on Spotify seems to come up with the full backlog from 2014 in reverse chronological order. I can't speak to the audio version but the book did have a large visual component as well, reflecting on the historical exhibits and the physical reminders of the past and what it tells us about German history and rhe nature of modern Germany. Endlessly fascinating and perhaps best as an introduction.

Mary Fulbrook's "Concise History of Germany", now in the 3rd edition (2019), is probably the best entry-level broad national history written by a renowned academic (in her case, the Cardiff University professor for German history) for the anglophone audience.

Other attempts at this have been made by James Hawes ("The Shortest History of Germany", 2017) and James P. Coy ("A Brief History of Germany", 2011). The quality of both of these books is also solid-ish (at least free of major errors), although I find both dwell a bit too much on ancient Germany and both end up writing their work a bit "too chronologically" (even including surprisingly lengthy discussion of the Neanderthals, which despite their geographic location should probably not be a major part in a German national history), whereas Fulbrook more consistently produces a solid work of history – no wonder, as she is the only one of the three to hold a notable academic career.

As for the specific continuity of Prussia, World War I and World War II — a bit specific of a topic to start with, I find — the continuity of Imperial Germany into Nazi Germany is a constant in the topics of historians of Germany. Heinrich August Winkler (formerly a professor in Berlin and Freiburg) produced the most famous (and one of the highest-quality) broad national history of that specific period in the form of his "Germany: The Long Road West", with an English translation having released in 2006. Specifically, you'll be mainly looking for the first volume, covering 1789–1933, with the Nazi period itself being covered in the first part of the second volume (1933–1990). Be advised though: Winkler's work is a notable step up in historiographical complexity from Fulbrook's work, and is clearly aimed at the historically literate German market rather than a foreign newcomer to German history.

Other good entries are "A History of Germany 1918–2014: The Divided Nation" (Mary Fulbrook, 2015), "A History of Twentieth-Century Germany" (Ulrich Herbert, translated into English in 2019), and "Rereading German History: From Unification to Reunification 1800–1996" (Richard J. Evans, 1997). All three of these works are fairly high-level, and especially Evans expects the reader to be already fairly familiar with concepts such as "Sonderweg" or the Prussian policy towards the Catholic minority.

But yeah, start with Fulbrook's "Concise History of Germany". It's a very convenient and approachable 300-ish pages, and it strikes a very good balance between noob-friendliness and historical rigor.

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