Yes, we all known Japanese children somehow manage to pick up the Japanese language from newspapers and books... :P
Think about how ridiculous that sounds. A 2 or 3 year old, beginning to speak, staring at a newspaper and sucking information from it. It simply doesn`t work that way.
Nor do native speakers learn a language in school in language classes - as is implied with the "an english class with an english book only about english". By the time you had reached that stage, you were already native-fluent in English. Things just needed to be polished.
You do not have that background with Japanese. You cannot jump in and expect things to go the same way. If you`re looking to LEARN Japanese, you`re going to have to make up for that other stuff. Immersion is much much more than being surrounded by written materials. If you were looking to improve already advanced Japanese - yes, a newspaper would be a good idea. But it sounds like you are starting from pretty close to zero.
I very much doubt your parents tossed you a bunch of newspapers and books - then left you without interaction to pick things up from them when you were learning English. The main component of immersion is
interaction - this is why some people who live in Japan but *do not interact* manage to be here for years and years yet never pick up much Japanese. This is also why children who have little or no interaction but who have access to books and television never properly develop communication skills. There are several key components to immersion, but the strongest one is interaction. Unless you have someone who will continually interact with you in Japanese, other components (books in Japanese, newspapers, Japanese television, etc) are not going to be of much help.
I agree that immersion is indeed the very best way to learn Japanese - however, unless you are moving to Japan, joining an immersion course, or your family speaks Japanese but just didn`t bother doing so until now... You are not going to learn much at the start from native Japanese materials.
But - if you really just want a bunch of Japanese books, magazines, newspapers, etc... I have a pile tied up ready to be tossed next recycling day that I would be willing to send you for the price of shipping.
Whether you would actually LEARN anything from them is another matter...