Upon seeing rule: "If the Death Note is burned or destroyed, all who have touched it will die." I'd probably hesitate destroying it. Then I would hide it, until Ryuk showed up to taunt me. At which point I start believing it might be real. We'd eat some apples, and discuss the universe. Maybe Ryuk would find me interesting enough not to kill me.
I cannot justify murder. And purging the sinful, please... anyone who thinks you should eliminate those who have sin has no idea what the concept of sin means. Salvation comes from the freedom to forgive and choose to stop sinning, not oppression to acquire safety. To add the words of another man in red:
"People who sin say this: They had to, to survive. People who sin say this: It's too late now to stop. The shadow called sin dogs them steadily from behind, silently, without a word. Remorse and agony are repeated, only to end up at despair in the end. But the sinners just don't know that if they only turn around there's a light there, a light that shines on them ever so warmly, a light that will never fade."