She was sworn in just over 100 days ago, so of course Governor Maura Healey still has a formidable array of unfinished business to attend to. Massachusetts needs tax relief, its frigid business environment needs thawing, its housing supply needs to be increased, its persistent outflow of residents needs to be reversed, and its obnoxiously opaque state government needs more transparency.

But also on the governor’s to-do list is a somewhat less daunting task: choosing a portrait for her office on the third floor of the State House.

By tradition, each incoming governor chooses the painting of a predecessor to hang in the Corner Office. As the Commonwealth’s 73rd chief executive, Healey has a lot of predecessors to choose from, beginning with John Hancock, who was governor from 1780 to 1785 (and then again from 1787 to 1793). To help her decide whose image should occupy the place of honor, Healey has invited Massachusetts students to submit essays about a former governor who inspires them.

Inspiration can come in many forms.

Healey might wish to celebrate the only other woman to occupy the highest office in Massachusetts by hanging the portrait of Jane Swift, who took over as governor in 2001 when Paul Cellucci resigned to become ambassador to Canada. Or she might pay tribute to a different predecessor with whom she has something in common. Paul Dever, a former attorney general, successfully ran for governor in 1948 — something no other AG was able to do until Healey broke the curse last year.

The new governor might give the coveted spot to a predecessor from the North Shore, where her family roots run deep — Healey’s parents grew up in Newburyport, and her mother’s parents met in Gloucester. Then again, maybe not: The best-known governor from that part of the state was Elbridge Gerry — a great Revolutionary-era patriot and one of the drafters of the Bill of Rights, but mostly remembered today as the eponym of gerrymandering.

Still another option for Healey, as the granddaughter and great-granddaughter of Irish immigrants, would be to honor the first Irish-American governor of Massachusetts. David I. Walsh, was also the first Catholic to occupy the state’s top post, serving two years as governor during the First World War; he later went to Washington as the first Democratic senator from Massachusetts since the pre-Civil War era.

Before she went to law school, Healey was an accomplished athlete: She was captain of the Harvard women’s basketball team, on which she was a point guard, then played professionally for two seasons in Austria. How fitting it would be, then, if she adorned the Corner Office with the portrait of another professional athlete who became governor of Massachusetts. Edward J. King, the Commonwealth’s chief executive from 1979 to 1983, played football as an undergraduate at Boston College, then spent three seasons in the pros as a lineman for the Buffalo Bills and the Baltimore Colts. Nor is athletics the only way in which Healey resembles King. He, too, was a Democrat who made tax relief an early priority and understood the importance of allowing business to flourish.

Healey probably doesn’t want to emulate William Weld, a former federal prosecutor, who had the portrait of the crooked jailbird James Michael Curley moved into his office when he became governor. Weld may have meant the gesture as a reminder of what can happen to dishonest politicians — or perhaps, as was often the case, Weld was just being mischievous.

The governor could play it safe by picking the portrait of a predecessor who was one of the Founding Fathers — Hancock, say, or Samuel Adams. Alternatively, she could signal her resolve to follow in the moderate footsteps of her immediate forerunner, Charlie Baker, by putting his portrait on the wall. (She couldn’t do so right away, though: It hasn’t been unveiled yet.) Or she might like to telegraph plans to run for a second, or even third, term by elevating Michael Dukakis above the mantelpiece: He is the only person to have been governor for three four-year terms.

If I were in Healey’s place, however, I wouldn’t choose any of these. I would go with the portrait of the only Massachusetts governor who became president of the United States: Calvin Coolidge.

In the popular imagination, Coolidge was a dour reactionary drudge, a dullard who said little and accomplished less. In reality, he was one of the most popular governors and great vote-getters in Massachusetts history, a witty man who had a gift for communication and cared deeply about public service. During his rise from Northampton city councilor to mayor to legislator to governor to vice president to president, he ran for office 15 times between 1898 and 1924 and “never failed of election,” as The New York Times noted in his obituary.

A man of strong ideals and integrity, Coolidge was profoundly concerned with social welfare. When he took office as governor in 1919, wrote Sheldon Stern, the longtime historian of the John F. Kennedy Library, Coolidge “supported a strikingly activist and progressive set of initiatives.” The list of examples is long, but they include endorsing the 19th Amendment to guarantee women’s suffrage, reducing the hours of the full-time workweek, increasing workmen’s compensation, drafting a package of proposals to deal with the postwar housing shortage, reforesting 100,000 acres of Massachusetts land, and creating a state Office of Fuel Administration to ensure that homes and businesses were heated in the winter. Coolidge had an admirable record on civil rights, condemning racial bigotry and the Ku Klux Klan at a time when the White House was occupied by the segregationist Woodrow Wilson.

In an address to the American Society of Newspaper Editors, Coolidge made his famous observation that “the chief business of the American people is business.” But he went on to make a more important point. “The chief ideal of the American people is idealism,” he told his audience. “I cannot repeat too often that America is a nation of idealists. That is the only motive to which they ever give any strong and lasting reaction.”

If Healey wants to share her office with a former chief executive who can inspire her to excel, she could hardly do better than to choose Coolidge, whose faith in Massachusetts never wavered. The Commonwealth’s 48th governor was one of its finest, and he would make a fine muse for its 73rd.