I use C++ as well.
C is fine for smaller projects and quick-and-dirty experimental stuff, but usually starts to get a bit unmanageable over 10k lines of code or so. Bigger C programs are certainly possible - there are perfectly stable million-liners out there - but writing C on this scale takes an enormous amount of discipline and usually involves reinventing many of the features of C++.
If you’re just starting with OpenGL, I’d recommend C or C-style C++. It’s a lot faster to play around with, just because it’s less restrictive. I normally try things out this way and then refactor the code into C++ classes when I’ve got a grip on what I’m doing.
That said, be careful when applying naive OO methodology to realtime 3D. In particular, lots of OO texts use the example of a graphics system which just maintains a set of abstract objects, each of which is entirely responsible for drawing itself. This is NOT the way to do fast 3D.