I voted for option 3, although I think there's a bit of option 2 there, and as some have said, Q did it for his own amusement, too. However, I think it amuses the Q to help humanity advance as part of a long-range plan whose real intentions only they know.
You see, by forcing the Federation to face the Borg then rather than later, they helped the Federation eventually learn how to combat a superior enemy in the form of the Borg. And the fact that they developed other advanced defenses to deal with the Borg means they could take advantage of these new defenses when it came time to fight the Dominion, as well. Think of the Defiant and its quantum torpedoes, which helped it ace Dominion fighter ships.
I see Q as a mischievious, almost sadistic instructor, like a Marine Corps drill instructor or like Professor Kingsfield from The Paper Chase
-- filled with good intentions but not caring to sugarcoat their brand of instruction.
Remember, Q did say in All Good Things
that the "trial never ends," and that the Q never reached a verdict in their first appearance. So the forced encounter with the Borg was part of this long trial.