Looking for opinions of 3d graphic programming

Question

I have done quite a bit of work in Matlab.  I picked up C# last year and have done some extensive programming there too.  I would like to rewrite some of my matlab 3d surface programs in c#.  As a math teacher, I am not to terribly interested in game programming, rather the ability plot a mathematical surface and spin them in space.  I would also like to be able to wrap an image onto a 3d object.  For example,  I wrote a program for my students for spereical trig.  They had to compute the launch angle to rendevous with the moon.  To illustrate the problem, and allow them to visualize what different angles did, I wrote a program that wrapped an image of the earth around a sphere and then had myself a 3d globe that I could spin in space and dipect multiple plane passing through it.   I would like to be able to control the alpha blending to adjust transparency.  I would like to be able to just send some kind of mesh of points to the engine and let it display it appropriately.  Is it easiest to do this directly from directx or opengl or get some external library.  I would rather not reinvent the wheel.  I would like open source if possible, but could put a couple of hundred down for a professional library if it was a good one and did what I want it to do.''