The quality of the image produced from the PDF can be changed by setting the
density (which is the DPI) before reading in the PDF - this gets past to
ghostscript (gs) underneath which rasterizes the PDF. To get a good result, supersample at double the density you require, and use
resample to get back to the desired DPI. Remember to change the
colorspace to RGB if you want an RGB JPEG.
A typical command line version for
convert might be:
convert -density 600 document.pdf -colorspace RGB -resample 300 output.jpg
If you need to crop it, a
-shave command following the resample is usually sensible, if the image is centred within the page.
As for the PHP IMagick extension, well, I never personally use it - so am unsure of how you specify file reading hints to it, but I would hope it is possible.