K&R and Stroustrup are classics, and eventually you should get them, but I don't think they are good introduction for C++ beginners. Thinking in modern C++ is thinking in classes, templates, exceptions, and streams, none of which available in C language.
I would recommend a college-level textbook on C++ like Deitel and Deitel.
After playing around, you should focus on learning to write a class that behaves like a built-in class. That means providing a copy constructor, operator=, operator==, operator<<, etc.. Along the way you'll meet various concepts embedded in the language of C++. I would agree with others on Effective C++ is a must read once you are comfortable with the basics.
