I have to admit to having UV/skylight 'protective' filters on all of my lenses. However, when I know that there is going to be no issue with damage, then I remove them. If nothing else, should a lens cap fall off in my bag, it can stop a fingerprint getting on the lens, thus one less clean that the lens requires. This is probably the more likely thing to cause damage to the lens, a bit of grit getting on a cloth and then wiped on the lens.
Dropping the camera/lens? I don't think that a filter is going to provide much of a crumple zone, then again, with a hood, I don't think they are going to be stiff enough to absorb that much of the impact anyway.
So, if on the beach, then I would keep the filter on. If out of the wind on a hill/landscape, then I could remove the filter (but would probably replace it with a PL anyway).
As to which is best, skylight or UV.
I believe that UV is more neutral. Skylight might cause a tint to appear.
On my more expensive lenses, then I would put Pro Digital filters. Some people on here have produced many examples of flare, mirror images etc. caused by cheap filters