I do a lot of machine applique, and I think the biggest thing that helps with the puckering is a stabilizer. I am super-cheap so I use magazine pages. They tear off fairly easily and you are recycling, too! Amma is right about making the stitches nice and close, too. Usually my magazine pages will fall off without me even having to pull on them.
I always cut my squares bigger and then trim them. It has saved me many times!
I have not used starch, but it does sound like a good idea.
Also, if I am laying a large applique on the quilt top, I will put some quilt basting spray on the back of the applique rather than pinning it. It is repositionable, but keeps it flat and stationary.