If you have a decent photo editor, you can set JPEG to 100% Quality and turn it into an effective TIFF file, but it will be MASSIVE.Yes.
your original artwork should not be 250 x 350. it should be at least five times the size. at a minimum 1250 x 1750 at 300DPI
#2 Don't downsize a JPEG. You will lose information. try to downsize either an original PSD, PNG, or TIFF, file. This way when you downsize it to 250 x 350 it will lose less information and not look too bad. a JPEG is already a compressed file so it'll look terrible when you shrink it.