The very best way of bringing new books to the attention of readers is to print a list of additions, with call-numbers, as condensed as possible, and with no other matter, for free distribution in the library.
In printing lists of books, make the classes covered special, not general.

Give lists suitable for as many different needs and occasions as possible.

There can't be too many of them.

For instance, a teacher would find thoroughly helpful and practicable such classified lists of books as, for beginners in third and fourth grades, for the intermediate pupils, for boys, for girls, numerous references to the current events of the day; historical readings divided into periods and adapted to different grades; historical fiction under several forms of classification; biographies and biographical sketches suited to different ages; geographical aids, including travel, description, life, scenes, and customs in different countries; natural history and elementary science; the resources of the library available for the purpose of illustrating topics in history, art, and science; material for theme studies; special lists for anniversary days now so generally observed in schools, and so on.
Lists in which the titles of the books come first are better liked by the general public than are author-lists.

People commonly know books by name, not by author.
Don't make the mistake of spending much money, at the library's beginning, for a printed catalog.