So basically when I assign a material to selection, because of the faces being grid-like, the material will have a really jagged zig zag edge. How do I get around this?
One way you could work around this is by using the knife tool. this can cut the white squares around into triangles that can be used to make the material flow a little better. you can do this by pressing k and then cutting out the shape. This should make it so you can have a better looking object. If you need any help with any of these steps, just ask.