In "Hamlet" why did the ghost appear to Hamlet?

I've always been confused, and fascinated, by the ghost.  Why would a ghost in purgatory, who wants to go to heaven by sending his murderer to hell, ask his son to commit revenge, a pagan act, thereby sending him to hell as well?

And why does it appear to Hamlet?  Most revenge ghosts appear to those that have murdered them.  Banquo appears to Macbeth.  Caesar appears to Brutus.  Why, then, does the ghost appear to Hamlet and not Claudius?

And the ghost exhibits double standards.  We are also forgetting that the ghost makes a deal with Hamlet: take revenge upon Claudius but leave Gertrude to heaven.  Surely, the ghost would want Hamlet to take revenge on Gertrude too, if not for accessory to murder, then surely for incest.

And the ghost appears twice to Hamlet.  Later in the closet scene, as Hamlet is getting rough with his mother, the Ghost appears again and tells him to back off.  Freudian (psycho-analytic) critics have had a field day with this reprise of the Oedipal Complex.

I tend to think the Ghost as an instrument of performance.  He has the best lines in the play.  He's an agent of in medias res, who awakens Hamlet's performance, the same way Mercutio awakens Romeo.  As critic Catherine England says:

Perhaps the ghost is a parallel to Polonius: a father sacrificing a child to a principle or a perceived greater good. The ghost doesn't reappear after Act III. Neither does Polonius. The functions of both are completed. Ophelia goes mad and dies. Hamlet, who was never mad, kills Polonius, comes to terms with death, and thus also with life, finally kills Claudius, and dies himself. Good and evil, life and death, married in one man, as is the true nature of mankind. Without the ghost, Hamlet could not reach that fulfillment of himself.