I have read that 1/4" per foot is the minimum fall for most residential DWV systems. I have also read that too steep a drain pitch can cause the liquid to flow past the solids. So, I'm wondering if 1/4" per foot is considered the ideal, or if I have room to do, say, 1/2" or 1", will the steeper pitch make a better draining system?

1/4" is ideal.

Whatever grade you choose, never install a drain pipe vertically. The solids will separate from the liquids in a heartbeat.

On a vertical pipe, which goes against the laws of gravity, the liquid or the solids?

m & m refers to flushing feathers fall faster in a vertical pipe.

That is an "old wive's tale", and if it were true, we would NOT be able to install any vertical drain lines.

Drop a pebble, a bucket of water, and a boulder from the top of the Leaning Tower, and see which one hits the ground first.

Sorry fellas, I should have included a or a to indicate "tongue-in-cheek". Drain line solids separation due to overpitch is a myth/urban legend in my book but it keeps rearing its head on this forum and the best way to beat it down is with a little sarcasm. My apologies.

some people would not recognize sarcasm if it ran over them with a truck.

if the truck was an F450 they would. and i'm not being sarcastic..