OpenGL! Yes I'm openly disagreeing with everyone on this board so far.
OGRE is a mess. The learning curve is steep. Yeah they've got some nice tutorials, but stepping outside the bounds of the tutorials and doing your own thing is VERY difficult. I'd expect to spend a three weeks before you can get OGRE set up and working, work through the tutorials, and figure out what to do next. There's nothing about OGRE that is THAT much better or simpler than OpenGL. If you are a good C programmer as you've claimed, and you understand your pointers/arrays/functions, OpenGL will be just as easy, if not easier.
That's why I strongly recommend starting with OpenGL. OpenGL will force you to learn all of the fundamentals of graphics. It's a lot more interesting as you'll actually come to realize what they heck is going on in the background. And YES start with NeHe's tutorials. Yeah they are 1.x which is very outdated (this is for you, Ranieri), but jumping into OpenGL 4.x is too steep a learning curve.
Start out with the immediate mode in 1.x (glBegin, glEnd), then learn about Vertex Arrays. If you want, play with display lists just to learn. Then move towards vertex buffer objects. Then learn about shaders. Each of these transitions are very easy, and there are plenty of great tutorials online. VBO's are in the core of 4.1, so by the time you make it there, you are no longer learning outdated material, and it's a lot easier to get there by starting with the 1.x stuff.
Also, if you ever want a game development career, nobody is going to hire you because you can make a cube spin in some off the shelf library. They are going to hire you because you understand what is going on at the lowest level possible and you can make design decisions based on that valuable knowledge.
References: I was where you were. I spent a month on OGRE, a week trying out Irrlicht, a week trying out Horde3d, two days playing with DirectX, and a month playing with OpenGL. After a month with OGRE I could barely go beyond the scope of the tutorials. After a month with OpenGL I had a character running around a minecraftian world, rendering 260,000 textured cubes per frame with 700+ framerate.