Do solid core doors reduce sound more than hollow-core doors?
From my experience solid core doors will block sound much better than hollow core. Solid core is also a heavier door which can be a plus although sometimes makes it a little more difficult to install.
Also, you want to make sure the door is pre-drilled for your hardware and pre-hung. The Jeld-Wen door you sited is a slab door and is not pre-hung. Slab doors need to have the hinges mortised and require more labor and knowledge to fit and hang correctly. So whichever type of door you go with (solid-core or hollow) make sure it's pre-hung.