I'm going to be honest here:

#Use your best judgment

Unless you're an actual diamond mod, your vote isn't binding. It takes 3x 20k votes to delete answers. So, even if you get something wrong it's a delete vote that's invisible to the mere mortal (you can't even see delete votes on answers until 20k, although they do confusingly show up in the 10k deletion list). Unless 2 other 20k users agree, it will just sit there (delete votes don't age away like close votes do). But the reason they gave you the power is that you've clearly done something right for a very long time. You're a long term user. *You should know what a good answer looks like now*. 

Furthermore, the community can make an answer undeletable by upvoting it. While questions can be deleted at any score, answers can only be 20k deleted with a negative score.

Last, but not least, you can always undelete. Nothing is gone forever (only Devs can do that wizardry).

Don't delete in these cases, tho

- **Rude or Spam** - Flag these. When enough people flag them Mods are notified for further action. If 20k users just delete them... nothing else happens.
- **Meh answers** - In baseball, a tie goes to the runner. In answers, ties should go to the poster. If you can't come up with a good reason for deletion *don't do it*. Don't stretch to delete. [Downvote bad answers and comment](https://meta.stackoverflow.com/questions/287563/youre-doing-it-wrong-a-plea-for-sanity-in-the-low-quality-posts-queue).

Also, if you're not aware, [voting to delete in the LQP consumes 20k delete votes first](https://meta.stackoverflow.com/questions/316010/stop-using-our-delete-votes-in-the-lqprq-when-20k-rep-users-recommend-deletion). It's dumb (once you're out of deletes it just counts them as regular votes) but it's how it works. It doesn't increase your LQP vote cap either (not that it's a big deal on SF.SE)