Long list of threads about using a filter or not. You decide which side of the glass you want to be on, if you want to use a filter for "protection" spend money on it.
Spend some money and get one that doesn't degrade the quality of the image, good luck with that though.
However if getting the absolute best from lens isn't an issue and it more about just protecting the lens then buy what you want.
Circular polarizers, neutral density and even a couple other special filters can offer help or desired effects in certain situations. But they don't live on the end of the lens.
For some people this bears repeating; a CP is for use only in certain circumstances and leaving it on the lens all the time is foolish at best.
A CP is a good thing to have when needed.
A UV filter makes a really crappy coaster, ash tray or magnifying glass but IMO these are all still better uses than placing one in front of my lenses.