Which is best, leaving a protective filter to on the lens and adding a circular polarizer on top, or removing the protective filter before installing the polarizer?

A Tiffen UV Protector filter can be kept on your lens at all times to protect it. It provides the added benefit of removing the excess bluishness often seen in distant scenes or shots taken over water, etc. You can mount a
Tiffen Circular Polarizer on top of your UV Protector if you wish, or you can remove the UV and replace it with the polarizer if you prefer–the results will be virtually the same.