Being that arcane tricksters are more utility casters than offensive ones, would Stinking Cloud be a good choice, or are there spells that are just better from a usefulness standpoint?

Well, first of all, you're going to need to be high level.  stinking cloud is a third level conjuration spell, so it eats into both your spell slots and your spells known of any school.

That being said, stinking cloud is a great spell if your enemies are all bunched up.  Even better if you're immune to poison, so you can get inside the cloud and no one can get you.  Free hiding and sneak attack.

Depends, I think if you have immunity to poison it could be pretty decent, but you could also replicate this with spells from lower spell slots (albeit without some of the extra utility like the poison damage). 

Personally I might generally use something else over it as a 3rd level spell, but could still definitely see use for it.

So there are caveats. I'm partial to spells that are fire-and-forget because I too easily get wrapped up in action economy. Maybe I'll go for Tiny Servant...