what is the difference of Texture Face Materials, Blender Multitextured Materials, Blender GLSL Materials? If I change to another setting all the behavior of my materials change - even some python functions are only available in some modes (e.g. setTexture). Why is that? Is there any advantage of one of these?
Blender GLSL material are the new kind. It uses GLSL shaders and require a graphics card that support OpenGL 2.0. With that you can use your materials. The other, older options work on older computer but has a much more limited range of settings.
Blender GLSL materials, IMO, would give you the best graphics but, once again, requires a graphics card that supports OpenGL 2.0. GLSL materials allows you to work with textures in a manner similar to materials outside of the GE. (Although, with fewer options since the GE doesn’t support all texture options at this time) The other two options are from pre-apricot Blender and textures in that can only be applied via UV texting. (I believe the GLSL supports Orco, no?) The GLSL also has Real-Time shadows with the spotlight, while the other two don’t. But also, as alienkid10 said, it’s a matter of preference and depends on how you want your game to look and how much your computer can handle.