"C++ is to C as Lung Cancer is to Lung."
C is a fairly simple and elegant language. Just to give a (very) rough comparison of the language complexities both languages have books written by their creators documenting the language.
For C this book is 'The C Programming Language' and in 274 pages you can learn everything you need to know about C -
http://www.amazon.com/C-Programming-Lang...0131103628
For C++ the book is 'The C++ Programming Language' and 1368 pages long...that is a striking difference and is a a good indication of the different in complexity between the languages.
Anyone that wants to promote C++ because it has OO functionality ought to refer to Alan Kay the guy who coined the term object-oriented:
"I invented the term Object-Oriented, and I can tell you I did not have C++ in mind." — Alan Kay
As mentioned earlier C is a very simple language, you have the normal control flow keywords, includes and compiler-time defines, you have the usual primitive types and you have structures, enums and unions. From that you can create everything and do so effectively with little overhead from the standard library.
C is a great language that works for everything the only complicated part of it for some is memory management and pointers it is not a bloated language with unnecessary features. It also forces you tot think much more simply about your problems and consider how the the code is going to be executed which makes it a good choice for learning how the computer works.
That said if you plan to go into industry programming C++ is quite common and a good choice to learn. There is nothing wrong with C though either; and odds are you could pick C up in a weekend after C++.
I'll end with one last quote:
"Historically, languages designed for other people to use have been bad: Cobol, PL/I, Pascal, Ada, C++. The good languages have been those that were designed for their own creators: C, Perl, Smalltalk, Lisp." — Paul Graham