What does a Laveyan follow?

Follows the principles and teaching of Anton LaVey and the Church of Satan in presently headquarted in California

Do Laveyans believe in God and/or Satan? Any God for that matter?

He does not believe in God or Satan, or any Being of Inteligence outside of
Man. Sees themselves as Gods already.

Do they believe in Good or Evil?

Clain to believe that nothing is good nor evil but the indulgence in self is foremost. However, in practice, LeVayian Satanist seem to still embrace many of the taboos and moral restrictions of the Judeo-Christians.

What are LaVeyan's opinions on other Satanism variants?

LaVeyan Satanists generally contend that they are the "real" Satanists, and that without LaVey none of Modern Satanism would be possible, as it was LaVey who "opened up the doors" to Satanism in the 1960s.