What kind of wall do I have, and do I need anchors?
For a 30 pound mirror i would not use just screws into plaster and lath. 

If your wall is as you state in the comments then i would use My favorite Toggle anchors 

They are very strong and have a beefy machine screw. 

You will need a 1/2 inch drill bit. You drill the hole, collapse the anchor, slide it into the hole, snug up the wall tab and break off the excessive part of the tabs, then just thread in the machine screw.

There needs to be enough room in the cavity of the wall for the anchor to go in and make its turn.

If your wall is plaster and lath there is a possibility that the back side where the toggle will be sitting against is not flat, this would cause the toggle to not be straight and aligning the screw to thread in may be problematic. 

Here is short but informative video on how to install.