I suggest learning OpenGL using a associated library such as freeglut or GLFW at first because the extra features offered by these libraries generally make your life easier. In fact, most tutorials offered on the internet seem to be specifically geared to using some form of GLUT, which again makes it a sensible choice.
Once you have an understanding of the basics of OpenGL you could do a small project which involves loading a model file (exactly which model file format I leave to you, but you could save yourself some work by using a format where the file import/export source code is freely available), and renders it to the screen. Then maybe think about adding in controls so that you can pan around the model, zoom in and out etc. If the model is animated then potentially you could draw the animation with a control to vary the running speed of the animation.
You could do a similar method with DirectX (in fact, doing it with DirectX would probably be easier, simply because of the sheer power of OpenGL), ultimately culminating in the development of a simple 3D model viewer.
You don't have to do a 3D model viewer, but it seems like a good comprimise if you ask me - Complicated enough to impress people but at the same time, not so complicated that you will be working on it for the next year before it is complete.