Try not to select images by using the magic wand tool, you will definitely get an image with jagged edges beacuse you're directly selecting the pixels, not the image overall. If you want to save your image with the foreground only as selection and in jpg format, as Etsuko mentioned, use the path tool and save it. You can always edit and create a smooth and accurate selection whenever you want to and the size of your file will be smaller.
Both are actually the same

There is another way to edge out or selecting complicated images like human hair by using the combination of Path and Channel. This is a PRO's technique and you need a lot of patience.