I make a lot of teeshirts for my granddaughter. These days I use the coverstitch on my serger to hem them.

Before I had this serger, however, I used to overlock the raw edge, then on the regular sewing machine, I'd put the widest twin needle and stitch it using a fairly long stitch (about 4mm). I did it with the right side up. On the wrong side, the stitch zigzaged and that held the fabric down. It resembled the cover stitch.

I also use a twin needle. The other thing that helps prevent stretching and the "frilly" look you are talking about is to hold your finger at the back of the presser foot and causing the fabric to "bunch" behind the foot. Release every few inches. This works really well.