I like most adventure path style with some extra content and freedom to roam around where ever we want to go. This forces "adventure path" be interesting. I generally like games with some plot, and strong theme, and freedem of choice. I also prefer games where you can as well become villains than heroes. Though I am willing to go for some more heroic theme too, if I like premise.
We usually tell who character goal is, then we tell what we really want our character become. Sometimes it's one of players who has best theme thought for game, sometimes it's invented by dm. One of my dm:s likes players to invent focus for game and sell it to him. If he likes it that's what we play. If not, new try.
However it's pretty easy to make some random adventures part of some story, like our another dm does. He changed all modules to relate some Moander cultist doing some evil stuff. There is theme, but plot is kinda what we make of it. Expecting to fight some avatar of Moander, maybe.
Problem with adventure paths and adventure modules of today is, that they aren't really that good. Not compared to some basic D&D and 1st ed AD&D adventures. Some of those were awesome, and partially because rules weren't so strict. And there was more pulp horror and scifi. I like that. Pathfinder modules vary in quality. Often they start strong and then go weaker. There are people who should never write high level modules. Especially those who don't like playing high level. Reason probably why adventure paths take you to lower levels than in beginning. My prefered gaming is 9+ levels. And all those names, before pathfinder I thought oriental adventure modules were once with "names that is hard to remember and everyone got them".