Though most (almost every) C++ compilers are fully compliant with C syntax, you may treat C and C++ as two totally different language, so there is no need to learn C before you start working at C++.
As considering to choose a programming language, it really depends on what do you want. If you just like it and not plan to choose software development as your future career. Then I suggest you study some scripts, such as JavaScript, VBScript and some Java. That can bring some interesting effect to your web pages.
If you are considering software development as your future career, I would like to suggest you study some C++. After you can do some coding and write some some simple applications, you'd better to study some important courses, say, data structure, principle of compiler, operating system, DBMS. What kind of programming language you are using is not important for a progammer.