Shine is nothing more than a surface with less imperfections. It looks nice and is primarily, in my opinion, cosmetic. You are not going to see it anyway and your first priority should be a flat surface before shine.
You can use the reflection to show a geometric pattern and look for distoration as an indication of where your base is not flat. But I would not use shine as your be all and end all indication of flatness.
There are conflicting opinions on the subject and some people might well tell you that a perfect mirror finish is not as good as one which is not. Certainly using a metal polish is going to introduce impurities and I personally would steer well clear of them.