Ogre 3d is great. It is under the MIT License and has many tutorials you just have to search through the wiki and stuff.
http://www.ogre3d.org/
http://www.ogre3d.or.../tiki-index.php
http://www.ogre3d.or...?page=Tutorials

And for input and sound I like SFML and you can use this for commercial or non commercial games whether they are open source or not.
http://www.sfml-dev.org/
http://www.sfml-dev.org/license.php

Also here is a tutorial I have used and it is great for starting out in SFML. It shows you how you can set up SFML and any other library in Visual Studios C++. It also shows you how to make a pong game with SFML.

http://www.gamefromscratch.com/page/Game-From-Scratch-CPP-Edition.aspx

Well, you have to choose if you want to use the low-level 3D library (OpenGL, Direct3D) which only handle things like drawing triangles, skinning etc. and program the advanced functionality (loading models, skeletal animation, et cetera). It takes a LONG TIME to comprehend (I would say 2-3 years at least to move to the current state of art technology), so be prepared. The upside is that you can make unusual games (e. g. space simulators) – the library won't limit you much – and you can fine-tune the graphics. Also take note that OpenGL and Direct3D (and drivers for them) are developed by professionals and don't suffer from "opensourceness" – known bugs and missing features not being fixed/added because the developers don't think they are important. The support is also much better because almost every programmer in game programming field knows one of them.

If you use the Direct3D, you can run your game only on Windows (and maybe Wine), so the best windowing library is the Windows API.

If you use OpenGL, you must choose a windowing library:

• Windows API (as demonstrated by NeHe) is not recommended to use. You lose your portability and it's messy.
  
• GLUT was a nice library, it has been discontinued by the author, but its fork FreeGLUT looked fine to me.
  
• I personally prefer GLFW, it is a lightweight library, so don't expect much, but it is clean and stable.
  
• SFML is another choice, but I found its documentation lacking and the library kind of new and missing important features. The sprite-manipulation API looks half-done to me at this point.
  
• Allegro and SDL are heavy-weight libraries, having 2D functionality, more helper functions and so on. I would recommend the latter as it has much larger community.
  

To summarize, if you just want a window created for drawing and input polled, use GLFW or FreeGLUT. If you need more from the library (2D drawing, audio), use SDL.

If you want to use graphics engines (Ogre3D, Irrlicht), you will have to cope with incomplete documentation, some bugs and inflexibility. But you will learn it (and make a game with it) much sooner than a 3D library. I used only Ogre3D and I have to say that it is a rapid and sufficient tool to make a game with. You can always modify it (MIT license). Some people say that Irrlicht is good, but I don't know.

In the end, the thing that matters is whether you want to make an engine or a game.