How do I properly bake a texture in Cinema 4D?
When you bake an object in C4D you get several options which passes you want to be applied in the final baked texture. You might want to try to generate new UV's by not ticking the "keep UVs" setting. If you want to bake lightning you have to tick the luminance pass for that.

Also be aware that the baked object might look horrible in the viewport but will look perfectly fine when rendered. Thats just a thing of how the OpenGL viewport is interpreting the material.

Though you're model does look a bit weird after baking. Are you sure this was a polygon object and not a nurbs object or a diffrent non poly object generated from a plugin and you are missing some interpolation? If thats the case you might want to turn it into a poly object first, maybe some subdivision setting differed for rendering and the viewport.