McKay, Scott and Whatmore all agree that the first appearance of SHE is as an illustrated serial novel in: THE GRAPHIC (London) from October 2, 1886 through January 8, 1887; Vol. 34 and 35, Nos. 879 to 893; and in HARPER'S WEEKLY (New York) from October 2, 1886 through January 1, 1887; Vol. XXX/XXXI, Nos 1554-1567. Each serialization is accompanied by excellent illustrations by E.K. Johnson, though HARPER'S WEEKLY only contains 9 of the 14 that are found in THE GRAPHIC.
The first authorized 1-volume book-form was published for sale in New York by Harper Brothers December 24, 1886. This Harper edition contains all 14 full-page illustrations by E. K. Johnson, as well as a double-frontispiece: two facing plates depicting the Sherd of Amenartas, drawn by Rider and his sister-in-law. McKay and Scott both agree on the American publication date.
The London first edition was published by Longmans, Green, and Company on January 1, 1887. The Longmans first edition purportedly comprised only 10,000 copies, each of which contains the same double-frontispiece as the New York first edition, but none of the E.K. Johnson illustrations. McKay, Scott and Whatmore all agree on the London publication date.
Longmans published its first illustrated edition, purportedly on November 1, 1888, which includes 32 illustrations by Maurice Greiffenhagen and Charles Kerr, 20 of which are full-page.
See the VisualHaggard.org page dedicated to the illustrations found in various editions.
I also own another first edition in original navy-blue cloth
Accompanying the book is a letter from HRH to Mrs Traquair dated December 14, 1887, regarding her possibly illustrating the at-the-time forthcoming 1888 edition of SHE (see below). HRH misspelled Mrs Phoebe Anna Traquair's surname, Traquiar.
A dissertation prepared by Elizabeth Cumming references a painting Traquair created titled "She" and dated 1887.