Bill Dunham faced similar questions when he picked Euler's best work from over 35,000 pages, over 800 works. He had experience, though. When he wrote his excellent book, Journey through Genius , he narrowed the field to just twelve great theorems in mathematics, and won awards for his efforts. These eight chapters, sandwiched between a Biographical Sketch at the beginning, and a few pages of Conclusions, make this a short book and leave the reader hungry for more.
Most chapters follow a fixed pattern.
First there is a Prologue, describing the state of a subject before Euler started his work. Finally, there is an Epilogue, which sometimes describes subsequent results, sometimes provides modern proofs of Euler's results, and sometimes sketches some of Euler's related results. One of my favorite chapters is the one on Analytic Number Theory, a chapter with a relatively short Prologue, because Euler virtually invented the subject. Dunham focuses on the results from one of Euler's earlier papers, written in 1737, when Euler was only 30. Dunham put that result in the chapter on Infinite Series.