As for the replacement, I've mused elsewhere that Rice is the obvious choice, but that wouldn't be for the purpose of setting up the successor, but rather to move Lieberman to State so that Jodi Rell (Gov of CT) can appoint a Republican Senator to that seat.
In any case, I would hope that the Democratic Congress, most likely the House, as Lieberman would be a reliable Republican vote, would hold the line until they get someone they want -- namely NOBODY. If Bush goes down to impeachment, he should not be replaced by a VP of his choosing. He should be replaced by Pelosi.