"Panels are great, but how do I change this one page?"
Panelizer means that instead of creating variants of node displays in page manager, instead you create variants of node displays in panelizer. This allows you to customize each view mode with panels. You can set a default layout for each content type and choose whether each content type allows for choosing different layouts on a per node basis.
There's a great presentation where the audio and video are out of sync. Other than that issue, it's a great video from Damian McKenna, one of the maintainers of the module and of Panels. The first half talks about panels and the second half talks more specifically about Panelizer. The talk about Panelizer starts with version 1, then shows what was added in version 2, after that it shows version 3's features, and finally it talks about future features (Workflow and Revisioning integration, for one), most if not all of which have been included since the video was created: https://www.youtube.com/watch?v=vy6fnsawNjE