Part of the reason why George W. Bush did not select the other candidates on his shortlist was because they were either too old/irrelevant (John Danforth) or had political ambitions for the future (John McCain and George Pataki). Politically ambitious vice presidents would mean a potential rival for Jeb Bush, which the Bushs did not want. In the scenario he does select Tom Ridge, the Bush-Ridge Ticket may be able to win Pennsylvania in 2000 (Gore's margin of victory was 4.17%) and in 2004 (Kerry's margin of victory was 2.50%). Dick Cheney is given a different cabinet position, either as Secretary of State, Secretary of Defense, Secretary of Homeland Security (when it is created). I think Secretary of State is most likely, because Cheney will be vital for selling the Invasion of Iraq to the public and to Congress. (I believe regardless of who is Bush's vice president, the United States would still invade Iraq because both Bushs viewed Iraq as 'unfinished business' and have a bone to pick with Saddam Hussein.) Cheney probably steps down from Secretary of State after serving 4-6 years. Ridge might be better for advising Bush on defense because, although Cheney served as Secretary of Defense, Ridge actually served in the military. Ridge also won't have a bad reputation for advocating torture behind him, as Cheney had.
Assuming the economic crash is not butterflied away, and Tom Ridge runs for president in 2008, his best option would probably be a conservative Senator, such as Sam Brownback, or conservative Governor, such as Mark Sanford or Mike Huckabee (moderate on economic issues). John Thune and Matt Blunt are good conservative choices, however, they are probably not experienced enough and/or lack name recognition. A good selection for a female vice presidential nominee would either be Carly Fiorina or Meg Whitman, but their lack of experience and status as former CEOs are liabilities.