I've read a variety of texts about Hitler and the Third Reich (William Shirer's work, Volker Ullrich's recent biography, multiple books about persecution of Jews and the Holocaust etc.), but I'd like to go direct to source. For example, I'd love to make use of the Nuremburg trials in a personal project, but I can't find full length English translations, only footnotes and references and select excerpts. Are there any translations of the Nuremburg Trials in a style similar to those available via the Library of Congress? Are there any other little-known sources which are of significant value to amateur and professional researchers?
The "best" primary source so to speak doesn't exist in any objectifiable sense. What primary source is useful for you is determined by what you are researching and what your question is / what you want to find out. There are document collections out there, some even with commentary and footnotes, but if you intend to research medical crimes of the Nazis the files of the Four Year Plan are not going to be as useful in finding out what you want to know in comparison to, say, the files of medical institutes.
In this sense, what is the "best" primary sources is determined by what you want to know.
In terms of what you are asking about: The Red, Green and Blue series on the IMT trial and the NMT trials are available in full online here at the Library of Congress. The Blue Series is the transcript of the IMT trial, the Red series is the documentary collection for the IMT trial, and the Green series represents both selected documentary evidence as well as transcripts of all the 12 subsequent NMT trials.
Harvard Law School is working on a project to make the full evidence used at both the IMT and NMT trials available online and searchable by key word but it is a work in progress and you are not going to find everything.
There are however several commented source editions out there:
Die Verfolgung und Ermordung der europäischen Juden durch das nationalsozialistische Deutschland 1933-1945, Edition, 16 Volumes by various. This ongoing project by the Institut for Contemporary History in Munich aims to publish commented and explained source documents of the Holocaust in 16 volumes covering virtually every occupied, controlled, and German-allied territory in Europe with one volume also planned to deal with Auschwitz exclusively. Drawing on perpetrator documents, documents by victims and by bystanders, the Edition publishes key documents as well as previously unpublished an un- or underused sources. An English Translation is forthcoming with the first three volumes in Germany slated to be published in 2018.
Hitler and the Nazis: A History in Documents. by David F. Crew (2005). Crew presents a history of the rise and fall of Nazi Germany through translated original documents. Includes various key documents from the Nuremberg laws to the Korherr Report as well as hundreds of photogrpahs and a very handy guide on what is a document and how to read it.
The Holocaust: Selected Documents in Eighteen Volumes. by John Mendelsohn (1982). A vast collection of translated documents, this 18-volume includes not only key documents such as the Wannsee protocols but also goes beyond liberation including volumes on the documents used in the Nuremberg Trials.
"The Good Old Days": The Holocaust as Seen by Its Perpetrators and Bystanders ed. by Ernst Klee, Willi Dressen, Volker Riess : A collection of writing and photographic sources documenting the Holocaust, through the letters, diaries, and reports of those involved and witnessing the crimes first hand.
Crew's work might be closest to what you are looking for since it includes key documents and doesn't require you to speak German. However, on the last thing a bit of a caveat: Not speaking German can be a serious impediment depending on what you plan to research. While key documents have been translated, for a variety of undertakings it is absolutely necessary to be able to read German in order to understand the vast majority of primary sources, in some cases also Polish or Russian. But the above should give you a clear selection of some important documents and in case of Mendelsohn also some additional info that might interest you.