I like soft and stable for SP bag projects. Love their designs and patterns but haven't made this one.
I trim the soft and stable out close to the tack down line so there isn't bulk in the seams. I have used no-show-mesh stabilizer and leave that in the seam line as it is not blulky. If I use cut away stabilizer, it is trimmed out of the seam line.
Just a tip for your class. Look at the PDF for the instructions relating to the bag size you are making. Check through the steps so you understand each one. Enjoy your class!