One of the best ways I've seen this done was in the Reagan wins in 68 TL here, with Brooke as his VP as a compromise to the liberal wing of the party, winning a term of his own in 76. One of my favorite moments of the TL was the Bicentennial of that TL, with a still popular Reagan taking to the event like a duck to water, and the year closing out with the election of the first black President.
He loses to Ted Kennedy in 1980, largely due to events outside his control - the economy, Iran - but he is still the first black President, and is fondly remembered on par with George HW Bush in OTL - as a good and decent man who, with the benefit of hindsight, probably deserved a second term. Brooke, in combination with 68 Reagan being much more moderate than 80 Reagan, ensures the GOP ITTL is more moderate than OTL, more liberal in some ways, more archconservative/libertarian in others.
As for other details... keep his home life more stable, his finances in the green, and get him re-elected in 1978. Given he lived until 2015 in OTL, he had the potential to be a power player in the GOP for a long time to come - even if he doesn't get the White House, I'd love to see him become a major GOP figure in the Senate, perhaps seeing other black Republicans come to power farther or sooner than OTL, like JC Watts, Colin Powell, Condi Rice, Tim Scott and Alveda King. Doug Wilder, who was always in the middle of the road on most issues, could well run as a Republican and win in Virginia.
In that scenario, it would be fun - with three decades of experience in the Senate, and having nurtured a generation of black Republicans, he runs for the GOP nomination in 1996, and with Colin Powell as his VP, defeats President Clinton to become the first black President.