From brainpickings.org I gather these were posters put out by Roosevelt's New Deal agency. ...Maybe they were trying to encourage people to use the library when they couldn't afford to buy books! ?
If you were going to do this, what book would it be? If I chose from the classics, I'd have to say Middlemarch cause I've had it kicking around so long (though Barb warned me against it.) Among newer books, I'd say Fall On Your Knees by Anne-Marie Macdonald, which is one of the books I brought to read here.
By the way, my mother was quite shocked by my 50 Books to Read This Year pile. She reads about a mystery novel a day. She doesn't understand this two-weeks-to-read-a-book business. Get in and get out!