I've been at two airlines and we did it two different ways, left to right, top to bottom and top to bottom, left to right. Whatever works for you.
In the Mooney I work left to right, top to bottom ending up at the emergency gear handle to check that it is stowed. We had a little extra panel space so we printed up short checklists and stuck them to the panel. They include only items that, if missed, will hurt either us or the plane. That does not mean I don't check other stuff, it just isn't on the checklist. We have one for before start, before takeoff, takeoff, after takeoff, approach, landing, after landing, and shutdown. We use them as checklists, not do lists. Do it first by memory, then read the checklist to make sure we didn't forget anything.
Bob