Rich, and anyone else interested in my opinions:
First, it might be well to remember that 11 of the past 16 Chief Justices that were nominated and confirmed, did not come from the Court. So it is nothing unusual for Bush to make this nomination.
A lot of people on the gun boards looked at Scalia or Thomas to have been nominated as the successor to Rehnquist. There are some very good reasons why neither were chosen.
Justice Scalia has not been a consensus maker. Very often, he is at odds even with his fellow conservatives. He has a tendency to write rather scathing remarks about opposition opinions, regardless of who they (the opposition) might be. He seems to respect no one, unless their opinion is in sync (if even partly) with his own. In this, he is contentious and is ill suited to bring consensus within the Court. An ability that Rehnquist had in spades (even when Rehnquist was the lone dissenter).
My own opinion is that I would have disliked having Scalia as Chief Justice for one reason alone. His tendency to hold precedence above reproach. This is most exemplified by his separate decision in Raich. An adherence to Stare Decisis, while generally a good idea, is absolutely wrong when decisions are made solely because of a previous decision. This has led to the creep of additional powers of the Federal Government, over and above what is Constitutional.
We have, as a group, often lamented upon the intrusion and expansion of the Commerce Clause. It is the root of all the Federal gun laws that we detest. And it can all be looked at through eh eyes of one decision in the mid 20th century: WICKARD v. FILBURN, 317 U.S. 111 (1942). I have often written about this seminal case, so I won't bore anyone with it here, other than to say that it was because Scalia would have had to revisit this case, that he decided to go with the majority of the Court in upholding the CSA. Even if Scalia had joined the dissent, Raich would still have had the same effect, only it would have been a 5-4 decision instead of 6-3.
As a Chief Justice, one would expect Scalia to side with whichever side was amenable to upholding prior precedent. Bush knows this. There are several cases coming up that Bush would want decided in his favor, but some of these cases would depend upon overturning prior precedence and Bush could not count on Scalia doing this.
Justice Thomas, on the other hand, would have been a more problematic nomination. If you thought that his initial confirmation hearings were bad, they would be as nothing compared to what a nomination as Chief Justice would entail. Most notably because in most all of his published opinions, Thomas has held constant upon the textual interpretation (what did the text mean when it was written, as opposed to what the text means now) of the Constitution as it applied to the case at hand. No one on the left would want a Textual Originalist to direct how the Court might proceed. Their beloved "living Constitution" might actually become dead in the water. Thomas relies upon Stare Decisis only when the text of the Constitution is ambiguous. That is most likely the way such things should be decided, but even here, Thomas has voted on more than one occasion to uphold the seeming expansion of Federal powers. While Thomas may be my personal choice for Chief Justice, even I have disagreed with some of his opinions (can't please everyone, yes?).
Bush simply doesn't have the political capital necessary to push for a Thomas nomination. Nor would he. It is already apparent to Bush that Thomas would not side with his administrations handling of the Gitmo prisoners. That alone knocked him off any list.
Other political concerns are that with O'Connor retiring, Bush really needs to find another woman to appoint to the High Court. Brown fullfills that criteria. Plus she is black and that plays into the race card and the left would be hard pressed to use that against her. But while Justice Janice Rogers Brown is a conservative, she is also a libertarian, when it comes to social cases. As a sitting Justice on California's Supreme Court, she has had many dissents on cases that would have (and did, many times she was the only dissenting opinion) expanded governmental powers to help the socially disadvantaged. She truly believes the libertarian concept of smaller government. She has routinely ignored precedent, even precedent set by the Supreme Court of the US. Like Thomas, she is a Textual Originalist.
Nominating her, would provisionally make Kennedy the swing vote, and he has often been so anyway. It would not upset the makeup of the Court all that much and perhaps would do more good in the long run.
But such a nomination would be fought tooth and nail by the left. I don't know that Bush could pull it off, as I said, he no longer has the political capital to spend. So while I would really love to see this gentlelady on the Court, in reality I don't expect it.
More than likely, it will be a surprise nomination, like that of Roberts. A virtual unknown that will be hard to make any case against, other than Bush appointed them.
So who could it be? Some speculate that Justice Edith Brown Clement (5th Circuit) might be in the running (although a few have used the label, "Souter in drag," in response to this...). Others think that Judge McConnell might be a good conservative pick. McConnell was appointed to the Tenth Circuit by Bush in 2002. McConnell was a Law Prof, prior to nomination. Others bandied about are Prof. Eugene Volokh (UCLA) and Orin Kerr (GWU).
Regardless, what it will come down to is who Bush is comfortable with. One of his most endearing attributes is his belief in his own judgment of character... And it may be his worst fault, at the same time.
An end note: Gonzales is not on any list, IMO. It would alienate his Republican base.