I use Kabnet deli paper. Found it at Sam's....2 500-sheet boxes for about $12....enough for a lifetime or two.
It has more body than tissue paper and tears off easily. You still get little bits stuck in sharp angles, but a pair of tweezers gets it all out.
Pin or spray baste the paper to quilt top and away you go. Especially nice when stitching over seams....with the paper on top, the foot glides across the seam rather than getting catching on the fatter part of the seam.
Haven't tried it with hand quilting but it may have too much body for that. Tear-away stabilizer might be an option here.