I would at least heavily starch the background fabric. You don't want to sew all the way around an applique only to discover you have more background than applique left at the end. I paint a 1:1 solution of Sta-Flo liquid laundry starch and water onto fabric until it is saturated, toss in dryer, then iron with steam before cutting the background squares. This makes the squares very stiff and stable so no stabilizer is required. The starch washes out later.
It's also a good idea to cut your background squares slightly larger than you want, then trim to size after your applique is finished.