from an intellectual/theoretical/analytical perspective, you should read Susan Sontag's On Photography, and Roland Barthes' Camera Lucida, if for no other reason than to understand why you disagree with some of what they say. For a history, there are quite a few books - the Beaumont Newhall book is a good overview but he has his biases (heavy favoring of the f64 school over the pictorialists, for one thing). I'll put together a more complete list when I get home and can scour my personal library for titles.
As for photographers who worked in the 20th century, I'd start with F. Holland Day, Clarence White, Alfred Stieglitz, Alvin Langdon Coburn, Edward Steichen, Paul Strand, Edward Weston, Manuel Alvarez Bravo, Lola Alvarez Bravo, Tina Modotti, Aaron Siskind, Minor White, Harry Callahan, Ruth Bernhard, Lisette Model, Wynn Bullock, Paul Outerbridge, W. Euegene Smith, Eliot Porter, Jan Saudek, Josef Sudek, Hiroshi Sugimoto, Martin Chambi... I can go on for pages In the list I've provided, I've sprinkled in a few folks you may not have heard of or thought about as much, because photography is truly an international art form and there are important people working in the medium outside of the US and western Europe who we should be aware of.