I don’t think short-term political calculations should lead the president to nominate a Chief Justice whose approach to judicial decisionmaking is far afield from what the president has endorsed. So I see Scalia and Thomas as the only acceptable candidates for elevation in the event of a Rehnquist resignation.
But if the president were to consider the political calculations that Kathryn’s correspondent raises, Ginsburg would be a better choice than Kennedy. First, I fear that making Kennedy Chief would cause him to move further left to try to establish a “Kennedy legacy”. Second, nominating Ginsburg rather than Kennedy would make any overall package appear more moderate. Third, nominating Ginsburg would reduce any undue diversity-driven incentive to nominate a woman to replace O’Connor. (There are, of course, plenty of women candidates who would be excellent selections on the merits.)
My guess, though, is that the Chief would be appointed from outside the Court.