When I've done machine paper piecing, I've always just used the cheap paper that I get in bulk for my printer from Staples to make my foundations. It's tedious and boring getting it out, but I've never had any damage to the actual stitching, and my machine is set to 2 for the stitch length, whatever that translates out to in reality.
I use a seam ripper to slit the large empty parts of the paper and do the rest of the removal with my fingernails, which are short, BTW. I don't worry too much about some of the shreds left in the seams. They won't hurt anything, and once you've got the back and batt under your top, no one will ever see those bits of paper again. If you're not planning on hand quilting in the ditch, they won't be in your way either.