CPL & lens protection

Let me start by saying that I have searched for a specific answer to this question, on internet as well as in this forum, with no success.

I have bought a CPL (Hoya) while purchasing Tamron 17-50 f2.5. I'm aware of suitable conditions to use a CPL. The CPL is good. To protect the lens from dust , water etc I want to put a 'barrier'. Can I keep the CPL all the time (since on non sunny days anyway it won't do anything) as a protection or should i get a UV / Haze filter.
I'm not sure how a budget/mid range US/Haze filter will impact the picture quality.

Thank you!

You can leave the CPL on all the time if you're willing to accept the 1-2 stop of light loss that comes with it.

A high quality UV or clear filter won't affect the image quality except under certain circumstances. I've seen cheap ones cause all kinds of poor image quality.

I just use a lens hood and install a CPL only when needed.