I got as far as Gen 2 when I realised this was fucking dumb and no one is going to agree with me anyway.
Team Regulars are exactly that. They appear in my team and stay there until I either have more than 6 regulars to choose from, or my hand is forced to cycle someone out of my team. Not all of these are competetive.
Prized in Storage are Pokémon that I like a lot, but have no interest in battling with. If I see one of these in the wild, I'll make an honest effort to catch it. If I have the patience, these end up being my Contest/Pokéathlon entrants.
Collectables are Pokémon I'm neutral to, and will probably catch if the moment arises; but they'll just rot in my PC, usually without a nickname. There are some Pokémon on here that I've actually not bothered catching, 4 Generations in.
Ugly Pokémon I never bother with. Either due to typing, moveset, or just because they look really fucking dumb. Most Fire types go here. I'll catch these only if I have no choice (for story-based things, trades, or for HM Slaves). A good number of these I've never even attempted catching. Fuck 'em all.