I'm going to assume that you don't want to read untranslated newspapers in Fraktur, because there are actually quite a few archived online.

I would advise reading Blackbourn's The Long Nineteenth Century: A History of Germany. It goes a bit too far back (it begins in the 1790s and has a bit of discussion about medieval Germany as well), but that could get you some of what you want in regards to Prussia. It also has a good bibliography of other works you can read, both similar general introductions or more specific works.

In addition to that, I would add the three anthologies edited by Evans (The German Working Class, 1888-1933: The Politics of Everyday Life; The German Underworld: Deviants and Outcasts in German History; and Society and Politics in Wilhelmine Germany).

As an addition, I would suggest Helmut Walser Smith's The Continuities of German History

Finally, I would suggest Christopher Clark's Iron Kingdom and his Kaiser Wilhelm.

To give a brief guide, Blackbourn's book is broadly a social history (concerned mostly with changes in society, ordinary people, and economic transformations) of Germany using Hobsbawm's scheme of the long nineteenth century (effectively that there were a set of transformations that occurred from roughly the French Revolution to the First World War that makes it a useful category to analyze with).

The three Evans anthologies and Smith's book are collections of essays dealing with different thematic topics from a social historic perspective. For Evans, this can be anything from street gangs during Weimar to rural infanticide. For Smith this is primarily exploring German conceptions of race and nationality looking for the underlying causes of the Holocaust in the long nineteenth century. I tend to think that articles in the Evans anthologies are a bit harder to read than Blackbourn, but often are just so interesting. I find Smith to be somewhere between the two. The only one that tells a complete history of Germany is Blackbourn though.

The two Clark books are more traditional politics histories, but quite good!

As a final recommendation, you might want to check out Mary Fulbrook's A Concise History of Germany. I've never read it, but I did read her 1918-2014 book and I liked it less than Blackbourn, but her A Concise History is more modern, is more explicitly introductory, and is, honestly, probably a pretty good textbook. If you want to go for something more difficult, I would suggest Eley and Blackbourn's The Pecularities of German History which effectively argues that historians have been imaging that Germany has been on a "special path" (Sonderweg) to the Holocaust and that by stop seeing Imperial Germany through the lens of outdated social theory a richer understanding of Imperial Germany can be made.

EDIT: Just to be clear, Evans is only the editor of the works I am suggesting. That's what makes them so cool. You can look up the authors of each essay and see what else they have written, but I tend to find the most interesting ones either didn't publish much else or published in German, so.