There's a lot of good questions and stuff in this post. As we know, I don't run a sandbox, so adjust accordingly...
From what I've been reading, it seems that in a sandbox campaign, the players' motivations is almost more important than in a traditional campaign since there are choices. For example, in an Adventure Path, there is essentially an unspoken agreement between the players and DM to follow the leads that are presented.
I don't run Adventure Paths, I write each adventure as a session, after finishing the last. So I'm always adapting to what happened last time, and extending the world. My group does tend to have the meta-game rule of "follow the plothook because the DM is lazy" but there is also an expectation of it must make sense for the party to do so.
In a sandbox campaign, do you think it's bad to tailor plots to the characters, and in some respect, the players themselves?
My style depends on it. On the first session, the plot hooks might be a bit weak, as we're all feeling the group out. But after that, I try to make sure NPC goals (hooks) intersect with the PCs. This is how I help ensure the PC will go for it, because I've done my homework and the hook is related to the PC, not just some problem the PC doesn't care about. I don't see why a sandbox couldn't use this trick.
If I'm creating a sandbox campaign for these characters, I can't assume that they will always help the little old lady across the street. I have to cater to their greed.
That doesn't mean I can't present choices to them that do involve going after the bad guys. If they continuously choose to ignore obvious threats, it may come back to bite them.
Thoughts?
As I said in another thread, "Good" PCs are predictable. Generally, if you present the PC with a princess in peril, they will go save her. Sure, there's a lot of variance on what the rescue will entail, but it's far more predictable than a non-good party.
Evil PCs (as an example) tend to do whatever. They're set of viable options in dealing with the Princess is wide open. They might save her, to build up a reputation as heroes. They might ransom her. They might do worse. The might even attempt the mission, see no profit in it, and abort the mission.
A sandbox style is probably a better model for an "non-good" party. Basically, expose a ton of opportunities for profit or whatever, and let them roll.
Somebody wrote a good blog entry on here about running a "evil" character. His point was to make opportunities for the PC to be evil without getting caught/having consequences. This in turn let the PC blend in as a 'normal' citizen in all the other encounters.
The real key is to make encounters/problems/hooks/opportunities that tie to what the player and PC wants to be doing in the game. If they're playing "good" heroes, give them heroic problems. If they're power-hungry, give them opportunities to gain power.