1. Set it in a mortar bed

I would never do that. What do you do when you have to pull the toilet for
some reason (repair, reflooring, etc)?

A bead of caulk around the whole underside of the toilet should be plenty to
keep it from rocking (once you replace the wax ring, as everyone else
indicated). I like to leave a gap at the back so that if there is a leak
in the future, you'll have some indication. If the floor is so unlevel that
caulk won't make up the gap, then I'd seriously be cursing whoever laid the
floor...

-Tim