The polarizing filter is used to cut reflections and darken blue sky making the clouds stand out. It is the most valuable optical filter you can own. It works its wonders, adding vividness without changing the colors of the vista.
While doing this task, it also functions just as a UV filter in that it cuts haze. The UV filter is universally used mainly to protect our precious camera lenses against scratches. The UV cutting benefit is of little value when mounted on a modern digital camera. This is because the digital senor is inherently very sensitive to UV light. The camera maker mitigates by incorporating a UV fitter into the protective cover glass mounted over the imaging sensor.
My advice is, never mount a filter if the harm outweighs the good. A filter adds two polished surfaces that reflect light. Reflected light is stray light.
Stacking filters adds additional surfaces. This reflected light intermingles with the imaging forming rays; thus it is the major contributor of optical flare. Flare can be devastating as it robs the image of some of its contrast.
The circulator polarizer adds four surfaces. The first is a linear polarizer; the second is a retarder to de- polarize. The first does the deed; the second prevents the first from interfering with the automation of focusing and exposure determination, as these can be challenged by polarized light.
Let me add that UV filters only work on far distant landscapes and high altitude aerial photography. They are virtually worthless at close distances.