I've taught many young girls to sew. I usually start with some sort of bag. Joanne's has some panels that are easy to cut and get the girl right on the machine. The second project i usually do is a simple garment that requires pinning and cutting. I have never used a "starter" machine, but I do put the speed on slow on the machine. Masking tape on the machine that goes from faceplate all the way down the front of the machine really helps keep the seams straighter.
Have fun!