If Beckett gets the job (and, considering how Old Labour Beckett is, that's an extremely big 'if' in itself) then she'll be no more than a temp for the next two years until Blair can groom a Blairite for the role. I don't see her as being that likely tbh.
Other possiblities:
- Robin Cook. A big cabinet heavyweight and a more likely possiblity than Beckett. Cook certainly wanted the job, but again, as like Beckett, he's Old Labour. But Cook would be a good choice if Blair used this as an opportunity to gun for single currency entry - Brown was the biggest cabinet opponent of that and Cook was the most pro-Euro member of the cabinet. But Cook was going through his divorce at this point and his reputation was already going down at the FO. An outside possiblity.
- Jack Straw. In my opinion, the most likely candidate here. Straw is a committed moderniser, has the experience, and is a 'yes' man. The only negative is that he has hardly any treasury/shadow treasury experience. But then again, a lot of Chancellors haven't when they've been tapped - Straw equally had no FO experience when he went there in 2001.
- Chris Smith. Now there's a thought. A better choice than Beckett IMO if you're angling towards Old Labour (despite him getting a dead-end portfolio in government, he had served on the shadow treasury team for five years in opposition and had had some big portfolios in 1992-1997.) and the first gay Chancellor would make waves. (Though that cuts both ways of course) But he's not really much more likely than Beckett ultimately.
Harman I left off, because she doesn't really have the gravitas at this point and had gone through an extremely messy incident in 1996 about where her kids went to school. She'd be promoted, but not to that sort of level. A possiblity to take over from Straw if he makes the move to Number 11.