Don't use a UV filter in conjunction with a CPL.
UV filters are a hangover from film. DSLRs don't need them for UV protection and there are no situations where they'll improve your images.
Using a UV or plain glass filter for physical protection is controversial and there are many debates about this on the threads, if you want to search for them. I've been involved in photography for over 40 years and I've always used a lens hood but, as a rule, I don't use protection filters and I haven't damaged a lens yet. I do, occasionally, use one in poor conditions if there's flying dust/debris/spume; if I remember to take one with me.
If you do decide to use a protection filter, make sure it's a good one. These tend to be expensive, but putting a cheap filter in front of your lens is likely to introduce softness and flare.