McCain - Would be the most likely due to being 'next in line' (a big advantage for various GOP primary candidates up until Trump). The GOP would also be desperate to win the White House after 12 years and he would be the obviously 'electable' candidate.
Huckabee - Only if he can gain traction. The faltering campaign of Fred Thompson in 2008 is what made him a serious contender that year.
Giuliani - Not likely to get though the primaries, not matter his 'hero' status. Would have to rely on McCain's campaign imploding.
Allen - I can't help but think of him in that category of overrated contenders in the 2000s and 2010s who went nowhere (aside from Allen, there is Warner, Bayh, Pawlenty, Huntsman, Walker etc). May well have dropped out prior to the Iowa caucus.
Whitman - Little chance. Would have been similar to Pataki's 2016 campaign.
Santorum - Would have likely be the choice of the party's right and would have a realistic chance if the party is in a certain mood (as it might have been during a Gore presidency).
Frist - Another Allen type candidate.
Engler - Could have been a dark horse and has the advantage of being from a big competitive state.
Thompson - I think Fred Thompson would have a better chance.
Nickles - Unlikely I would have thought.
However, unless Gore had some kind of major eff up he'd probably win re-election, which might make the 2008 primaries between Romney and Jeb! for the Republicans and Lieberman and Hillary for the Democrats.
9/11 would have damaged Gore.
How so? I think he would have handled the aftermath with much more competence and not been dragged into a senseless and costly war in Iraq.
There's even some chance 9/11 doesn't happen in this timeline because it's being prevented. There were warning signs in advance and the Bush administration after getting in scaled down the efforts of the Clinton government to hunt Bin Laden.