The short sermon 🙂
JPG is a lossy format.
Should be used as final output only, for web or email, etc.
If image started out as JPEG, like from digicam, not much you can do about that, but save the original JPEG untouched. Make all edits and resaves as PSD or TIF. If you need to output another JPEG, go back to your PSD or TIF (or original JPEG) and output from that, rather than JPEG to JPEG.
Although PDF DOES have a good usage for printing….if you have added text, and it is still in a text layer (TIFF/PSD), saving as PDF will retain the vector nature of the text and will print sharp regardless of the resolution you’ve used in the file. Also preserves vector shapes.
Mac