My 0.02, even though you have previous programming experience is to start with C on a linux box so that you can focus 100% on learning C. Then make the leap to C++ and WinAPI because otherwise you will be learning both of them at once...just IMO, but I think it would far easier and will be much better off in the long run. Especially if your interest is doing lower level stuff with Windows

And I agree that the C programming language book is also very good, definitely pick it up