Case: 1
Let’s say my site’s name is “thingamajigs” and I have a category called widgets. What would the optimal title tag be?
thingamajigs | categories | widgets ?
thingamajigs | widgets ?
categories | widgets | thingamajigs ?
categories | widgets ?
I certainly wouldn’t put the word ‘categories’ in there - it is just filler and contributes nothing to the title, just wastes space (and top-billing space if you put it at the start).
I generally go for “site | section | page” order, but it will partly depend on the nature of your site and how you expect people to use it.