How often does your game touch on anything close to that, anyway? Either very rarely and that's wasted space on the character sheet, or almost exclusively and you're missing out on all of the other stories you could be creating.
Depends, honestly. In an ideal old school game alignment means almost nothing (i vacillate between it reflecting behavior and it being purely a metaphysical tag, and a righteous paladin could be chaotic, his actions furthering the goals of chaos on a timescale no mortal can comprehend ). But, as you get high level, you start factoring more directly in the divine conflict and inevitably they get you involved.
But i don't like alignment in general, i think its often restrictive, and very few good characters fall into one category or another.
Anyway, I'm actually starting a game this week. Online, but with people I know so not the usual online experience. Going with a homebrew setting, a flat world with the sun in the south and no moon. No tides, no real seasons (the southern continents are always hot and it gets colder and darker the further north you go, with obligatory Evil Zone in the farthest north where sunlight never reaches)
Don't have any guidance for players at the moment, setting it up as a kind of pseudo uexcrawl. There's a successi9n war on the northern continent and the lack of manpower means monsters and bandits in civilized lands, and private mercenary bands are becoming profitable. Gonna start in medias res with a monster hunt that'll lead them to the starting semimegadungeon and give them some side hooks to keep exploring it. Having fun with the dungeon.
Main 'plot' aside from the war is that the continent to the south is ruled by a cabal of sorcerers from another world, akin to the masters in eador. They know how to take control of shards and are working to annex the players' world. Have a few hooks for getting involved there floating around