I don't like to sew, either, and I do have a zipper waiting to be put into a vest (since Christmas
You want the kind of zipper that doesn't separate at the bottom. The separating kind are used for sweaters that zip up. I've found that Joann's is good for zippers. I'd suggest that you wait until the bag is done before you buy the zipper so you have the exact measurement that you need.
As for the sewing machine? I don't see why not, but your mom is probably a better judge of that.