Anytime you add something in the optical path you will lose quality. The quality you will lose depends on the filter quality, filter type and lighting conditions.
Most filters are extremely susceptible to flare because they add a flat reflective surface and can take a great image and make it completely unusable. That does not mean you should never use a filter or even more than one, but you should do so for a valid reason knowing the sacrifice you are making at the same time.
Polarizers have specific usage and an effect which cannot be simulated by software, so use them to cut-down reflection, increase saturation in the sky, etc. No need to add it over another filter that essentially does nothing.
UV filters have a use too but are rarely actually needed. They are usually recommended at high-altitude but AWB or custom white-balance takes care of that. Since they are cheap and do not cut-down light by much you can use them to protect your lens when it is in eminent danger such as near salt-water and flying sand.
Against knocks, a lens hood is much more effective protection and may even increase image quality by reducing flare from stray light.