Answer:
jpeg format IS a high quality format when created or saved as 12% (or 120 depending on application) - it has the same quality as a BMP or TIF with no compression artifacts
a low quality jpeg cant be made high quality just by converting the file format - the amount of work involved in improving the quality of a highly compressed jpeg usually isn't worth it and you still end up with an inferior image than if you just start out with a high quality image to begin with
when working with jpegs in photoshop or other programs always save as 12 (or 120) and you will get no compression artifacts (those annoying blocks of pixels) - most better digital cameras save jpegs as 8% (or 80), occasionally as 10% (or 100) which is good enough for most uses but be sure anytime you edit the image you save it as 12 so you don't further damage the image
as a digital photographer i shoot exclusively in jpeg format and my camera saves at a 10% compression which makes those pixel squares almost unnoticeable and i never had a complaint about image quality