My suggestion is to start by learning "pure" C++ with the help of a good book (I can recommend Accelerated C++ by Koenig and Moo, I think it is ideal for you, because it gets to the point fast, it is correct and it uses a modern idiom).
If you do take the often suggested "Thinking in C++" book, remember that it is quite dated, and the author is more keen on Java/C# than C++, which sometimes shows. The code examples often use dated idioms, and are sometimes inelegant, and (rarely) even wrong. All that said, it is still a good book, fun to read, and the author is a good teacher. Just remember to double check the examples and take them with a grain of salt.
Afterwards start with learning Qt if you want to do GUIs, I think it is a great UI framework. Qt uses a preprocessing step called MOC compiler, which makes it kind of a language extension, which solves some practical problems, but is considered to be kind of a Hack.
At least (IMVHO) Qt is much better than most native Platform frameworks (MFC, Cocoa), and you're code is portable to most major platforms.