Sometime during each weekend. Arrington Liggins Dixon opens his bedroom closet door and lines up his suits in the order he will wear them -- the blue pinstripe on Monday, the brown plaid on Tuesday, the gray sharkskin on Wednesday...

It is neat. It is orderly. It is precise. It verges on being prim. It leaves little to chance. It is the way Arrington Dixon runs his life. It is the way he will try to run the District of Columbia City Council.

Dixon will be sworn into office tomorrow, right after Mayor-elect Marion Barry, as the council's second elected chairman, and -- as he notes with pride -- the first native Washingtonian elected city-wide to a top municipal office.

It is, he says, a culmination of ambition born in an Anacostia boyhood, and a detour from a career that first took him into the military and then down parallel roads as a computer specialist and a lawyer.

Now 36, after two elections and four years as Democratic councilman from upper-middle-class Ward 4, Dixon clearly was in the right place with the right credentials when broader opportunity knocked early in 1978. Sterling Tucker was vacating the council chairman's post to make what became a futile run for mayor.

Douglas E. Moore, a maverick at-large councilman noted for slashing attacks on the city's business community and carrying a reputation for sometimes - erratic behavior, had announced for the chairmanship Dixon, with a sedate manner and a reputation for hard but plodding work that contrasted with Moore's stridency, followed suit.

With business support. Dixon took the Democratic primary by a 3-to-2 margin and went on to win the general election against only token opposition.

Approaching the new job, which casts him as a referee among a dozen other individualistic council members with widely varying philosophies and temperaments. Dixon professes to have no specific legislative Program -- no list of "must" or pet bills designed to achieve his own political visions.

In an interview the other day, Dixon described himself as "largely a public manager of a board of trustees... (with) a responsibility to try and pull together the many different factions... I think of myself as a team player, but I will initiate."

Characteristically, one central aim is a matter of image: "I want to help the District of Columbia as a community to be property viewed in the country and the world. There are misconceptions about the living city (of Washington). It is a world city and a national capital, but it is also a living city."

If this improved imagery can be achieved, Dixon said, it should "create an atmosphere conducive to ratitication" of the D.C. congressional representation amendment by the remaining 35 states needed to add it to the U.S. Constitution.

Dixon refused to drawn into speculation whether he might run for one of the House or Senate seats created by the amendment. Neither, in a separate interview, would his wife, Sharon Pratt Dixon, the city's Demoeratic national committeewoman, daughter of a prominent Superior Court judge and herself a lawyer who works for the Potomac Electric Power Co.

John A. Wilson (D. Woard 2), a council colleague and professed admirer of Dixon, foresees a limitless future. Asked where Dixon will go politically, Wilson did not pause before replying: "Anywhere he wants to go."

Dixon already has gone from modest but genteel surroundings in a boyhood apartment on Shannon Place in Anacotia to an unpretentious but spacious five-bedroom ranch-style house of red brick in the North Portal neighborhood, hard by Rock Creek Park west of 16th Street NW. From his front porch. Dixon could hurl a stone scross the line into Montgomery County.

Did the move from one of the city's most impoverished sections to one of its most affluent represent an uprooting?

"Not at all." Said council member Willie J. Hardy (D. Ward 7), who represents much of the area east of the Anacostia River. "Arrington has not moved away from his roots -- his roots are in this entire city," Hardy said.

His parents were transplanted. His father came from North Carolina, his mother from Madison County, Va., north of Charlottesville, where a family compound in the Blue Ridge footbills is known -- from her family name -- as Afrington Estates.

His parents, James Washington Dixon, 72, a retired Exxon gasoline distribution plant worker, and Sallie Arrington Dixon, 68, a retired health services supervisor at the Masonic and Eastern Star Home, live with Arrington's family during the winter and in Virginia during the summer.

This produces a special family bonus, Sharon Dixon said -- a closeness between grandparents and Arrington and Sharon's two daughters. 10-year-old Aimee and 8-year-old Drew, both pupils at the neighborhood Shepherd School.

Dixon himself was close during boyhood to his brother James Walter, two years his senior. Together they played on the grounds of Cedar Hill, the Frederick Dougass estate, and joined in the activities of St. Philip's Church, then a new Episcopal parish in Anacostia.

They also talked of politics. Dixon recalled. "We made a commitment to each other, that if ever there was an elected (city) government, we would like to be part of it," he said. "James was going to be the candidate and I was going to be the (campaign) manager."

Meantime, Dixon became active in the Diocesan Episcopal Youth organization. He became a volunteer speaker for the United Givers Fund, traveling around the city extolling the value of charity to youth groups. In 1968, he was a delegate to President Eisenhower's White House Conference on Youth.

After graduating from Douglass Junior High School, Dixon went across the Anacostia River to attend McKinley High School.

There he did something that was to shape his life in two ways. Emulating an uncle who was an Air Force colonel, he became active in the student military cadet corps. It ultimately led him to the Air Force Academy in Colorado Springs, by appointment of then-Rep. Adam Clayton Powell (D-N.Y.). And it reinforced the sense of personal order and precision that remain his personal hallmark today.

"You have to have order to accomplish high standards," he said. Lapsing as he frequently does into computer-age jargon, he added: "You have to have systems to maximize or optimize."

In 1964, his brother James died in the crash of a military plane in the Philippines. Crushed by the loss, Dixon was asked to resign from the Air Force Academy when his grades plummeted. He did, ultimately enrolling at Howard University, where he studied computer science and met his future wife. They went together three years before marrying.

After getting his degree, he taught at Washington Technical Institute, now part of the University of the District of Columbia. Encouraged by Sharon, he earned a law degree from George Washington University, but never has practiced.

After losing his first bid for public office, a seat on the Board of Education, Dixon became one of 15-Democratic aspirants in 1964 for the Ward 4 seat on the elective city council created by the new Home Rule Charter. He won nomination with 20 percent of the vote, and subsequently was elected.

Because council terms are staggered, he had to run for reelection in 1966. It was an easy victory

As a new council member, Dixon was regarded as an almost hyperactive introducer a sponsor of bills. One successful measure created postcard voting registration. Another liberalized the city's divorce laws.

Named chairman of the council's Government Operations Committee, Dixon began overseeing deliberations in 1966 on a landmark two-inch-thick bill that will reshape the city's personnel system. By 1980, the city's 44,000 employes will be virtually divorced from traditional ties to the federal civil service.

At council sessions, Dixon always appears impeccably groomed, wearing aviator-type eyeglasses that replaced horn rims a few years ago. Unlike Marion Barry, whose suits are of a somewhat modish European cut, Dixon affects the traditional Brooks Brothers look (although he says he spreads his business among several stores).

One big need today, he says is for black youth to fit into society in appearance as well as manner.

"I am not presumptuous that I'll be a role model, but I hope I can." he said. "We don't need to be promoting Superfly -- let's not make the barriers even greater.'

If his preselected ensemble permits, Dixon likes to wear something green, reflecting mild personal superstition that the color invites good luck. (He even spent hundreds of extra dollars during his campaign for chairman to print a green dot over his last name on all posters and brochures.)

Standing a fraction of an inch under 6 feet, Dixon keeps his weight at 185 pounds by bicycling and walking and an occasional set of tennis.

His main commitment, both he and Sharon declare, is to the black community and to jobs and economic growth.

On economic matters, his wife said, she would describe Dixon in the moderate to conservative spectrum, but on civil and human rights she would rate him as an activist.

His wife added that she and Dixon keep their professional ives apart -- she never lobbying him for legislation either in behalf of Pepco or the Democratic Party organization, he never intruding on her role as a staff lawyer for the big utility company.

Dixon has made the Metroplitan Washington Council of Governments the principal instrument for seeking economic goals for the community. Elected chairman of COG early in 1978, he steered the organization into a program aimed at regional economic development. Only by such broad measures, he said, can future jobs be assured for area youth, city blacks and suburban whites alike.

The Dixons, by their description, lead a quiet, close-knit family life, eating breakfast together each day since professional life is making increased demands on theirevenings. They say their personal social life is limited. A favorite activity is have a few friends over for dinner and conversation.

Dixon does little recreational reading. Mostly he reads technical manuals on computer sciences ("to keep track of my professional field") and articles about city management matters, he said. For escape, he will occasionally pick up a book of science fiction.

A red "hot line" telephone in his spotlessly neat home study is rigged so that, with the push of a button, he can call any council member without dialing the full number.

And down at the District Building, where he likewise maintains an uncluttered desk, he has ordered the installation of quorum bells in council members' offices. In this way, he hopes he can lure the congenitally tardy legislators to meetings on time.

Will it work? "I don't know," Dixon replied with a shake of his head. "All I can do is set a tone."