For machine applique, I like to heavily starch the backgrounds so I don't need to use a stabilizer underneath. Starching also helps me make more accurate cuts.
Instead of spray starch, I use Sta-Flo (liquid available in stores with laundry supplies) diluted 1:1 with water. I "paint" on the starch using a medium-sized house painting brush, toss the yardage in the dryer, and then iron with steam. This makes quite a stiff and stable yardage.
When cutting the background pieces for applique, I cut an inch or two larger than needed. After the applique is done, I trim the block to exact size. (Learned this the hard way, after four pieces ended up with less than 1/8th of an inch available for seaming!)
Mary