"Illumination" information is generally not transferred with a model.
In Blender, you're likely seeing the textures (images used like decals on the surface of the model), but the "lighting" won't be stored with the model.
What you might be experiencing is that the textures aren't being saved with the model, so when you open it with Noesis, it's just black or gray. Textures can be saved with the model, but you will have to tell Blender to do that. OBJ is really your best option, at this point. It will store basic model and texture information, and is very widely supported. You can make sure that it is exporting what you want by checking these settings ("Write Materials" is the important detail, here):
This other answer has a good set of instructions for how to export a Blender model as an OBJ. It'd be worth your time.
It also sounds like you still have a lot to learn. It'd be worth your time to watch every tutorial that BlenderGuru has, or at least every modeling tutorial. Covering all the basics will make the learning process easier.