Learning C++ for building an application

[Zyxl]

I'm about to begin developing an application that requires some basic 3D rendering, so I'm looking into C++, as this seems to be the usual language for this type of thing and I have a book to help me with this project that includes some snippets of C++ code (not essential that they are understood, just useful). I plan on developing everything myself without the use of libraries like openGL (like I said, the objects and materials will be very simple).

However, I don't know any C++, but am familiar with many other languages (if C++ turns out to be impractical I shall use Java). How long would it take to learn and could I learn as I go along? I can compile and run very simple files, but I don't know how difficult producing a project would be and about dependencies and libraries I need (basic libraries only). Also, I would like to know if I can develop and do some testing on Linux even though my final program will be for Windows. Do I just need to change compiling settings depending on which OS I will be using?

Thanks in advance.