Playing devil's advocate, because I think C is a good starting point...
Personally, I started learning with C, algorithms, data structures, memory allocation, file manipulation, graphics routines... I would call these the elementary particles of programming.
I next learned C++. To over-simplify, C++ adds the layer of object-oriented programming - you have the same objectives as you do regardless of language, but the approach and constructs you build to achieve them are different: classes, overloading, polymorphism, encapsulation, etc...
It wasn't any educated decision on my part, this is simply how my programming course was structured, and it worked out to be a good curriculum.
Another simplification... C is basically a subset of C++. You can "do C" with C++, by avoiding to use the language features of C++. From the perspective of language features. Libraries are different matter. I don't think you will get past more than just programming 101 without beginning to use and build libraries, and there is enough out there to keep you busy for a lifetime.
If your goal is to learn C++ ultimately, then beginning with "C" could be a logical start, the language is "smaller" - but there is so much in "C" that you would probably want to narrow your focus. You are tackling a bigger beast, but if you get guidance, I see no compelling reason not to, despite the path I took.