As promised, I checked the owner's manual for my pump today and it said that it could be mounted horizontally or vertically. But if mounted vertically, ensure that the pump head is pointed down, with the electric motor on top, so that "in the unlikely event of a leak, water cannot enter the electric motor case," as I expected.
And I still maintain that an old soft foam-rubber mouse pad works well as a cushion between the pump mounting base and the mounting surface. It absorbs almost all the vibrations from the pump and keeps it much quieter. I did this to our pump and it is now whisper quiet. And the suggestion to replace the hard plastic lines with soft flexible hose (with a loop in each, to absorb vibrations) will add to quieting things down. Those hard plastic lines transmit the vibrations to anything they touch, resulting in more noise.
Hope this helps!
Mike