For transferring designs onto quilts: use Gladwrap Press and Seal.
It will stick to whatever you want to trace and then stick to the quilt.
After you're through quilting just peel it back off the quilt.
Lap size quilt sizes for adults: 56x70, 60x 75, or something in that area of measurement.
Machine quilting tips:
Use your fingers and hands to guild the quilt not your arms to move the quilt under the needle.
A single-hole throat plate may help in stitches at curves.
A presser foot with shank angled to the side and open in the front for greater visibility.
Needles:#70 Universal to start learning on, then switch to #70 sharp and then #60 sharp for tiny, precise holes. If using #60 sharp use thread that is #60 cotton two-ply silky cotton embroidery thread for top and bobbin. But if you use heavier thread then a larger needle is needed, like a #70 sharp or jeans/denim needle. No polyester thread for machine quilting.