Yeah, Buffy should do her job and slay the damn thing as soon as possible.
Vampires should be killed because they literaly wear the fact of their victim, the soul doesn't seem to be able to pass on. So even if they're helplesss i.e- just rising up from their graves- then she should stake vampires before they do what's in their nature.
Demons are a bit trickier since it depends on if they hurt people or not. Some have very human qualities that imply 'soul' so she shouldn't kill them if they are neutral/balancing types.
99.9% of vampires are dangerous and should be staked. That's her job. The two anomalies she knows of are different circumstances. Other than Spike and Angel, harmless vampires don't exist! She's made mistakes in the past by not staking vampires she should have at the time (Drusilla, Harmony etc).
Demons are different. We know there are peaceful demons, a lot less of them exist than evil demons, but IMO Buffy has a responsibility to protect these creatures from harm from other demons, not to do them harm herself. Who is she to pass judgement on them? Sure, she's the slayer, but unless they post a threat to humans, they should be left in peace.
As far as actual Watcher policy, which would be about the closest thing to any sort of ethical rules under which a Slayer would operate, I would say that there is only one: "If it's a vampire or a demon, kill it." Beyond that, the Slayer would be bound by whatever her Watcher says. I don't believe that there ever was any sort of official prohibition against killing humans, whether they be evil or just innocent bystander, if it became necessary or expedient.
Of course, we all know, that ain't Buffy by a long shot. That's probably why Giles never bothered to give her that infamous "Slayer's Handbook" that Kendra referred to.
As far as I know apart from the obvious almost all vampires are soulless, so she would need to kill them asap before they killed. As for general demons, I think there are some with souls like Clem, so I don't think those innocent ones should be killed, they can't help the way they look.
I think that Vampires should should be killed period . The only good ones we know of is Angel & Spike so kill them all is good.
But there demons out there who nice . Clem is a good Demon to use as a example.