well, the way I organize them varies from game to game...
usually, I would change the box settings so that every background is used, then name the Box to the type of background it is.
Then I would organize pokemon into whatever background they fit in, with my main team, HM slaves and other important pokemon in the Pokecenter box.
I may also have boxes for breeding pokemon, or pokemon I have bred, or a favourites box, or if I'm lucky enough, a shiny box for shiny pokemon.