I use mainly copy paper. I would not use water, it will just make the paper harder to remove.
You should shorten your stitch length when PP, it helps stabilize the stitches while tearing the paper away and it also makes tearing easier. I fold the paper and then put my hand on the main part and tear the pieces off with my thumb and index finger. I do not have any trouble tearing it and have very few pieces that stick in the seams on a whole quilt top. I will remove the little pieces in the seamlines, at the intersections, as I sew the rows together, leaving the rest intact until the whole top is done. It is easier to get those little buggers out at that time then when they are all stitched in :D:D:D