Really quick question (I hope) before I buy Maya I want to know if it has the option of exporting coordinates for triangle vertexes rather than images. If it doesn't, is there software that would allow for modeling while exporting vertexes for 3d triangles?

Why don't you get the free trial, play around with it and see what you can do, then buy it.

And I'm 100% sure it exports model files (with all the vertex info) rather than images. Not sure why you would think that it exports just images.

What are model files, and how do I use them in the context of an opengl application?

You are going to buy something that costs $3500 and you don't know what it does? I have never worked with model files in OpenGL (yet) but it will just be all the texture coords, vertexes, normals and all the information needed to draw and move the model.

I have no intention of buying it until I have "done my homework" thus the reason I am posting here. I was just wondering about its exports (I have learnt most that can be known about its interfaces and abilities that I could find online) because I am working on a C++ header file for OpenGL Vertex Buffer Objects using only triangles and was wondering if the exported model files would be all triangles, or if it would be a mix (making VBO's harder to use) basically if somebody could help me find out more about the Maya model files (usage and content) that would be greatly appreciated. Thank you.

if you don't know the terms used by these products and systems, how can you ever hope to determine whether they're right for you?
There's tons of books and no doubt websites out there to help, get searching and you will be enlightened.