Would there even be an Iran-Contra with HW in charge?
Deficits will be smaller here.
The Republican Party likely trends more toward the center, despite the high expectations placed on Bush to further Reagan's conservatism. Foreign policy matters such as the Cold War and Iran-Contra Affair are handled slightly better than OTL.
Bush probably doesn't pick Quayle or the Doles. On January 20, 1985, Quayle would have only been a Senator for four years. I remember reading elsewhere on this site that Bush didn't pick Bob Dole because not only was Dole viewed as baggage from 1976, Bush and Dole secretly blamed each other as having deprived one another of the nomination in 1980 (more likely than not, Dole runs in 1992 for the Republican nomination against whomever Bush's VP is for the nomination.) On January 20th, 1985, Elizabeth Dole would have only been Secretary of Transportation for less than two years (more likely than not, Bush retains her from the previous Reagan cabinet.)
Many people on this sight concur Paul Laxalt is the more likely choice for Bush's VP, given his conservatism and friendship with Reagan. Howard Baker would be a pretty solid choice, but Bush probably wouldn't pick him because he doesn't bring regional balance as a Southerner, nor ideological balance as a moderate (more likely than not, Bush gives him a role in his administration. Whether or not it's OTL's White House Chief of Staff is moot.)
Jack Kemp, while providing regional balance and considered right-wing in the 1990s, was considered a moderate in the 1980s. Bush probably nominates Kemp to serve as his Secretary of Housing and Urban Development during his second term.
Center is relative.
The overall economic trend on both sides of the aisle was towards the right from the late 70s onwards and this trend held across countries. Deregulation, deficit reduction, free trade, privatization, tax reduction, and tighter monetary policy were an international norm.
Bush would probably be more deficit-minded though, meaning that if there is 1986 tax reform it won't involve as steep tax cuts and would focus more on tax code simplification.
I'm not sure what GOP social policy would be.
On Abortion, HW's 1980 views before joining the ticket were... (1)Opposed to abortion, but opposed to a constitutional ban of abortion; (2)Opposed to federal funding for abortion; (3)Supported the right to an abortion in cases of rape, incest, or threat to the life of the mother. Barbara Bush was pro-choice, but kept quiet about it.
On AIDS HW signed the Ryan White CARE Act (federal AIDS/HIV funding) and the Americans with Disabilities Act (which protected people with HIV), but he didn't do much on top of that.
HW Bush was a drug warrior. This also rippled over into HIV/AIDS Policy (opposing needle exchanges and whatnot).
HW was for taking some action on climate change in the early 90s. Cap and Trade was under him IIRC.
HW and Reagan were both fairly liberal on immigration.
Most of the shift right on social policy since the 80s seems to have been bottom up.
I wonder if Laxalt is nominee in 1992. He'd be 70 years old.