Basically I don't know what settings to select when exporting obj.

I think it broke again, it's not properly writing the mtl file, I got it to export half-right but now it's all white again.

Now, do you have any clue how I should export the OBJ so everything links properly?

Nope wait just a second, I have another update! So, the thing you said about things not being packed into the blend file might not be true. After I closed and re-opened it al the textures do stay. I googled a little and it led me to pressing: File - External Data - Pack All into .blend.; and then File - External Data - Unpack All Into Files. That gave me a folder of png textures I am seing in blender (!!!) After exporting an obj I now have at least half of the textures being properly linked by the mtl file, and the other half appears white.

I see, damn. Sorry for wasting your time, I guess I will have to abandon the idea after all. Thanks for taking the time to dig through this mess.

Your explanation is a bit too complex for me to understand, so could you answer this instead please. At this point I think I might be misunderstanding the difference between materials and textures or something. Forget about the map add-on. Let's say I make a new blender file and import medic.mdl. He gets imported not as just a white object, but fully colored with appropriate materials. And when I select Shading I can see there is something resembling "nodetrees" you mentioned. So what's going on, is that not something that can actually be exported as a PNG along with OBJ?

So what's the explanation for me not being able to export textures for a single model either?

Well, me being a noob, I can't comprehend how it is possible that the texture doesn't exist anywhere yet blender displays it perfectly fine. I assume BleST lets Blender read VTF files but not export them or something? Manually converting them is obviously not an option since I'm working with a whole map which has tons of materials.

I'm trying to export through File - Export - Wavefront (.obj) (I can see how my previous comment can be misread, what I meant is I imported a random TF2 model with BleST and tried to export it nto .obj)

I can't get materials to be exported along with the obj for a model that was imported into blender using BleST. I once imported some random 3d model from the internet into blender and exported obj with materials without issues, but I can't get it to work for models imported with BleST, or that other add-on for maps.