I use french seams when I don't want them to have raw edges.
I used a 2.25 inch binding on the seams on the last bag I made. For the box corners, I folded in the ends of the binding and covered the raw edges. The top edge was also finished with binding and covered the raw edge of the binding on the side seams.
I have the Ovation serger and love using it to finish edges too. Easy to thread and set-up.