@theev's Jerry Brown TL is a good picture of Brown's potential, in the right climate and with proper campaign discipline -- but OTL's 1980 primaries is a good picture of how grandly and quickly Jerry could come off the rails. He sits on more of a knife edge than any other candidate of either party but he'd surely run.
We have done purely speculative Ford-wins threads like this before so this is not even a new list on my part but it is I hope a good general accounting for the 1980 campaign:
DEMOCRATS
Walter Mondale -- He's the likable VP candidate and icon of stability from Carter's flameout, he's Hubert Humphrey's protégé, and he has eyeball-deep union connections when that was still a major fundraising source for Democratic candidates. Not perhaps the most inspiring or nimble candidate but he's in very good position to make a go of it.
Hugh Carey -- Absent Teddy he's the absolute go-to Catholic Democrat candidate, and can stand on his defensive but successful "economic miracle" saving New York (city and state) from its debt. He's a big, gregarious guy, an admirable widower, a Keynesian and backer of unions, and a pragmatist of broad appeal.
Jerry Brown -- What more that might need be said about the governor of California will be said by thousands; everybody's got an opinion about Jerry, it's his blessing and his curse.
Reubin Askew -- The Southerner with the best chance of making something of himself after Carter's flameout, more charismatic and on some important issues (notably civil rights and economic populism) more sincere than Carter was at this point in his life. A deeply honest and remarkably decent guy for a politician, if he's made it into the Senate after the governor's office ITTL because of the more favorable legislative environment for Democratic candidates he's got a solid resume as well. Has the potential to be a regional power that might break through and at the very least high, high up an eventual nominee's VP list.
Scoop Jackson -- Scoop's '76 campaign was a lead balloon (sandbagged in the end with no little skill by Hubert Humphrey, who teased entry to the PA primary just enough to kneecap Scoop and leave the nomination either to a breakthrough liberal or Carter who would then have to have liberal support, like for example The Hump's junior partner Fritz Mondale...) But he could chance it this time around especially since Frank Church was up for reelection and likely to keep his head down leaving room for a NW/Westerner (California being West Coast but sui generis.) Depending on what's up in the Middle East Scoop's hawkishness and deep knowledge of energy policy could be a good sell. At the very least, like Askew he could "run for Veep' very effectively. (There are some stories that he stayed out in 1980 on a gentlemen's agreement that he would be Teddy's VP if Kennedy did primary Carter.)
Ed Muskie -- I think there's a decent chance the Old Man of the Mountain gets into the mix. He was by then disillusioned with the Senate and looking for something else, he was in a different way but just as much as Moonbeam a "premature New Democrat" ideologically, but he was Catholic like Carey and had good relations with the AFL-CIO. Plus by now his famous '72 flameout had turned into something much more like buyer's remorse. There's a very good chance that he rolls the dice and enters the primary.
REPUBLICANS
Ronald Reagan -- Because of goddamn
course he does. And why wouldn't he -- he's the messiah of the New Right and the natural challenge to Vice President Dole, age and 1976 be damned.
Bob Dole -- The sitting Vice President is going to set himself up as a force of inevitability and the most loyal Republican party man around, but 1980 may not be the year to play that game for multiple reasons.
Howard Baker -- Beloved across party divides in the Senate, people had been telling Howard he should run for president for years and 1980 presented the best chance of his career to do so.
John Connally -- A Mitt Romney with charisma and a deep resume, the moneybags of the primaries and the other natural Sun Belt representative besides Reagan, and a Nixon man to boot. ITTL he might have looked at running for governor again in Texas in '78 (particularly if in Cabinet reshuffles Bill Clements was promoted to Secretary of Defense from his deputy spot, or quite possibly Secretary of Commerce.) Connally actually has more baggage back home thanks to people who either thought he was insufferably vain and moderately corrupt, or those who thought he was a damnable turncoat. But he still had rivers of cash and a remarkable career to conjure with, and as governor would have been in a stronger position than IOTL. At the very least he's going to make himself an indispensable Veep candidate by way of his primary campaign.
Phil Crane -- It was a vanity project from go IOTL and there seem to be few exogenous influences that would have pushed him otherwise in the broad contours of this TL. There to keep Reagan "honest."
Liberal to be named later -- Could've been John Anderson as IOTL, could have been Lowell Weicker who very nearly ran. Longer odds on Charles Matthias or John Chafee but they're still on the fringe of possibility.
Then of course in each party there's the chance of an extra, outlier candidate or two, or variations (ex. if Muskie stays out and winds down his career I'd say there's a chance John Glenn gets in instead. Otherwise it's too crowded with big players and Glenn might as well hold out for the second spot.) But that's the broad ambit of candidates, I think.