I am making my first game with 3D graphics, and I wanted to decide on a graphics library before I do any graphics work. I am using C# VS Express 2010. I have seen suggestions for XNA, Tao, and just plain OpenGL or DirectX. What graphics library would be best for beginning graphics?
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Your question is extremely broad, and open to many different opinions, but I'll offer my own anyway.
Personally if you're new to 3D game development, I would start with XNA, it has a very clean wrapper for DirectX that takes care of the mundane details and lets you learn and prototype 3D games very quickly. That being said, XNA isn't a graphics library, it's just an API. Graphics libraries tend to do a lot of the work for you. However, there are nice graphics libraries for XNA that you can use, or full game engines with graphics systems built in.
Here are some graphics libraries for XNA
And here are some game engines
Sunburn Engine, starts at $150, although I believe there is a free trial
QuickStart Engine, free to use, uses JigLibX Physics Engine, no level editor or animation implemented yet
Engine Nine, free to use
And there are a handful more engines as well.