Our games are similar to what IronWolf said. I try to get the characters to do their own thing in the beginning so that they can begin to define themselves, but soon after, I throw out some hooks to begin a story. I usually have one or two overarching goals, with many possible directions and let the characters decide how to proceed.
If I'm running a Maptools campaign/game, I usually have to set up the story more firmly so that I'm more prepared for the games. It is much harder to improvise when online gaming because I like to use maps so the players can see what's happening, and I pre-program the tokens with macros so setting up takes a little bit of time. My players understand, so they kind of accept the "railroad" tracks. Some times I can let them get off the track, especially when they are in a roleplaying situations, and that may influence how future games (or encounters) will play out.
If I'm running a live game at the table, it is much easier to improvise and let the characters run with it. I have lots of possible maps, or I can draw one on grid paper to suit the situation. If they want to sail to an island that is rumored to have gorgeous women who serve their guests and impart gifts to their visitors (of course there may be a catch), rather than continuing on their way to a nearby town to deliver an item to their patron's ally, I let them hire a ship and go.
I guess it just depends. I would check all of the options in the poll.