Does anyone know how to take your work from DAZ Studio to a JPEG image without loosing picture quality ?

Just render to a JPEG with 80% quality. Anything 80% or above will generate images with no quality loss.  Or use PNG instead, which has lossless compression.

if you want a decent quality
render larger than the viewport   ie:- render to file or new window.
for print render to at least 3000 pixels on the longer side. (depending on size of print)
for upload to most galleries render at 1200/1400 pixels on the longer side.
save as .tif format.
for upload to online gallery convert to .jpg using a good app
( 'export as' , from the file menu in PaintShopPro, 'save for web' in Photoshop, Gimp has something similar and i believe there is a free app called 'picture resizer' available)
most galleries have a file size limit of around 5/600 Kb.
a picture rendered at 3000 X 3000 pixels can still look good, on screen, compressed to 500Kb.

my usual render size for most images is 1200 pixels on the longest side.
hope that helps.

Thanks Everyone