This is what it looks like with material preview. You can see that the face skin becomes transparent so you can see the mouth and eyes through the skin. This is wrong.
Any advice would be appreciated. I got this model from DeviantArt, so I don’t know how to edit in Blender that well yet. Is there any simple way I can fix this?
If it looks like how you want in solid preview, render it like that. Either with view->viewport render image/animation from the 3D viewport menu, while in solid preview, or by changing your rendering engine to Workbench, in properties/render.
Otherwise, I’d think that it would be hard to understand what’s going on when you’re first starting, especially considering there could be multiple issues interacting. If you’re interested in Googling to advance your knowledge, some of the issues here could be alpha blend mode, z fighting, and material transparency.