I've struggled a lot with myself over whether I should use OpenGL or Direct3D. There is no blanket answer to this question that anyone can tell you. Both APIs have a very different feel and which one you prefer can only be decided on your own.
Although Direct3D seems more structured and honestly makes more sense to me most of the time, I find the barrier to entry is much greater than that of OpenGL. With OpenGL it's easy to find lot's of great tutorials that help you get started, although the there are some outdated tutorials which teach you the old way of doing things. Sorting between the two of them is the hardest part. The modern way of doing things is with buffers and shaders.
OpenGL of course has the advantage of being multiplatform but I would say don't let this influence your decision too much. I've had working with OpenGL on some kind of Linux system on my list of things to do for some time and I still haven't gotten around to it. 95% of my programming is done on Windows and if things are the same for you then it doesn't matter if Direct3D is only available on Windows.
OpenGL is a C based API which makes it easy to P/Invoke into from C#. You can use something like OpenTK if you want, but for my needs I just P/Invoke. I'm working on my own C# OpenGL API which I call Samurai. It's not a 1 to 1 binding like OpenTK but an attempt at creating a higher level API for OpenGL.