The names (“Isabel Scott Stone” etc.) appear to be set in Cushing, later also known as Cushing No. 2. Mac McGrew writes that this face was “cut about 1897 by ATF” – if the ID is correct, Cushing was around at least a year earlier, and this poster would present an early use of it. In 2020, Font Bureau released Custer, which is a digital interpretation by David Berlow, reviving the name that Barnhart Brothers & Spindler had used for their copy of Cushing.
The other text elements are probably lettering, not type. “March 1896.” is in a thin and wide style with spur serifs. Some details like the high center in M and the sloping stem in a are a bit similar to Della Robbia, designed by Thomas Maitland Cleland based on 15th-century Florentine inscriptional capitals and released around 1902 (and hence after this poster was printed). The last line with the sender information (“The Shortstory Publishing Co.”) is rendered in a monolinear slab serif. Small differences in the repeating letters (see especially the spine of S) suggest that it’s hand drawn.