Thanks for the great question. I am gearing up to teach the second American core this summer so these suggested texts are excellent starting places.
Welcome to H-SHGAPE, the online forum of the Society for Historians of the Gilded Age and Progressive Era and one of the founding networks on H-NET. H-SHGAPE seeks to encourage the study of the Gilded Age and Progressive Era through its network and online resources.
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Great question! I typically teach The Gilded Age every couple years, and I change the course every time.
I've used Jane Addams, Booker T. Washington, Jacob Riis--the usual suspects, I suppose. I've also used a 1903 issue of The Independent called "The Concentration of Wealth" to good effect. That volume also contains material on Gen. Smith and the investigation into the Samar massacre during the Philippine Insurrection. I've also used material on the 1877 Great Strike here: http://railroads.unl.edu/views/item/strike_77
University at Albany, SUNY
I have actually benefited enormously from the ever-growing supply of digitized primary documents. When I taught the PROGE last, I incorporated the history of my university town (Binghamton, NY) and had students read about a local Cigar Strike, the Endicott-Johnson Shoe Factory (a company town), and a terrible clothing factory fire that killed 38 young immigrant girls. It gave students' first-hand examples of PROGE themes while also encouraging them to connect with the city in which they live.
My students get a lot of mileage out of Jane Addams' "The Subjective Necessity of Social Settlements" (1892). This initially surprised me, as I wasn't expecting students to connect with Addams, given her penchant for world travel, her support for expansive government action (I teach in a conservative area), etc. However, a substantial number of my students relate to Addams' description of the frustrations of young women with older generations telling them their dearly-held beliefs are precious and unimportant, and the reading always makes for a good discussion.