Mayor Marion Barry proposed yesterday a $1.5 billion budget -- up 8 percent -- for the District of Columbia next year, calling for no ne taxes but the reduction or elimination of some key city services.

The budget, which Barry called the "first statement of some of my priorities, policies and proposals," would reduce the school system's budget by nearly $10 million, eliminate the jobs of 216 policemen and institute a trash collection system east of the Anacostia River that would result in one weekly collection instead of the current two.

The budget, for the fiscal year beginning Oct. 1, 1980, would also close three neighborhood health clinics and impose a $25 patient fee for Medicaid abortions in order to help reduce city spending.

The proposed budget calls for a reduction of 1,397 regular jobs in city government, while increasing the budget for Barry's personal office operations by 23 percent and that of the City Council by 14 percent.

At the same time, Barry's budget proposal would provide nearly $5 million to help renters buy homes and for the city to purchase and rehabilitate other housing that would later be rented to low- and middle-income persons. The budget would also nearly double the amount of District money that the city spends on programs for senior citizens.

Barry would continue -- at reduced levels -- his summer jobs for youth program and provide nearly 2,000 year-round jobs for students, school drop-outs and young adults with dependents. There would also be additional spending for tourism marketing, consumer affairs, women's and Hispanic programs and projects for the arts.

Standing in front of a half-dozen multi-colored graphs outlining the budget, Barry proclaimed that a "new direction" had been launched in city government. He conceded that his plans for new programs had been tempered by the experience of nine months in office.

"It's just very difficult. I'm the first to admit it," he said.

Barry said that city residents would have to understand that their municipal well was in danger of soon running dry.

"We can't furnish everybody with everything. We can't pay for everything everybody wants," he said. "We've taken from those who have and given to those who don't have. But those who have are fast running out."

Barry said many of his recommendations are designed to meet congressional approval rather than pursue ideological or political points.

"You have to make some decisions about what you can win and what you can lose. We've been losing a few with our budget," Barry said. "This budget strikes a balance between what I want and what some people in Congress want."

The mayor's budget, which must still be approved by the City Council and Congress, represents an 8.1 percent increase from the $1.4 billion budget for the fiscal year that began yesterday and that will end next Sept. 30.

The budget would not require an increase in the city's current property tax rates, which range from $1.22 to $1.54 per $100 of assessed value. But contrary to his proposals of 1977 and 1978 when Barry vied with other mayoral candidates to offer the greatest tax relief, this budget would retain all of the increased revenues the city would bring in from assessment increases.

Barry administration revenue analysts expect assessments to increase by nearly 13 percent during the next year. As a result, property tax bills would probably increase by an identical average amount.

Barry abandoned as unrealistic the city's two-year-old push for an unprecedented -- and never granted -- $317 million federal payment. He said, instead, that he would work to establish a formula that would fix the level of the federal payment each year. Such an arrangement would be more efficient, Barry said.Yesterday's budget requested $300 million, the maximum amount now authorized.

The major fee increase would be a doubling from $5 to $10 of the fine for many parking violations, including violations of the city's commuter parking ban and illegal parking in metered spaces.

The city would also increase the license and examination fees for physicians, create a new $3,500 class of liquor licenses for nightclubs that would not be required to serve food, and change the way that banks and savings and loan associations are taxed.

The budget also includes $187 million for capital improvements projects, $30 million more than allocated for the previous year.

Among the major capital improvements projects proposed are $26.7 million for the downtown convention center, $11.3 million to provide public works improvements for construction of the Capital Gateway housing development in the Buzzard's Point area and $10.8 million for paving, sewers and drains at the Fort Lincoln new town project in Northeast.

Barry also plans to spend $6.1 million to replace antiquated gas lines in nine city run public housing projects, $3.7 million to renovate the East Capitol Dwellings housing project, $4.9 million to purchase the old National Lutheran Home and use it as a senior citizen facility and $30.5 million for a new crosstown water main.

The mayor also requested $17.6 million to pay the city's share of Metro rail construction costs and $2.7 million for Metro bus subsidies.

The Barry budget would barely keep pace with the 11 percent inflation rate forecast for 1981. It would use new management approaches to avoid tax increases while launching new programs.

For example, the proposal to change trash collection procedures east of the Anacostia River is designed to save nearly $700,000. Similar approaches have been used in Atlanta and Tampa.

Residents would be given free 82-gallon heavy plastic trash cans with wheels attached that could hold up to a week's garbage at a time. The new cans would allow the city to use two-man rather than three-man crews in the area and make half as many collectors. Thirty-eight jobs would be elimated. The area east of the river was chosen because it has fewer row houses and more paved alleys, city budget officials said.

In wards one and two -- the downtown, Southwest, Adams-Morgan and Mount Pleasant areas, a private firm would collect trash instead of the city. This, too, would save the city money, city budget officials said. Nearly 70 positions would be eliminated.

Barry's proposal would reduce the school board's budget to less than it was in 1978. It is likely to be a controversial proposal politically because the mayor is quietly supporting several candidates for the board in next month's election.

When he ran for mayor last year, Barry said he would have more authority to improve the schools as mayor than he had had as school board president from 1972-1974 because he would propose the school budget. Yesterday, he cited a projected 12.2 percent decrease in school enrollment between now and 1981 to support his proposal for less school spending.

"Everyone has to take their share of sacrifice. It's a tough time," Barry said. "There's no way you can continue to expect, when our school system loses 6,000 people, that the school system should get the same amount of money."

The budget reduction would eliminate 839 positions. The school board, which determines its own spending programs within budget limits and employe ceilings set by the mayor and City Council, would decide which positions to cut.

Barry contended that the school reduction was small compared to that of the Department of Human Resources, the city's largest agency, which was alloted $40 million less than its director had said would be needed to maintain services at current levels.

Among the proposed reductions would be the closing of three community health centers: Arthur Capper, 1011 7th St. SE; Parkside, 701 Kenilworth Terrace NE, and Northwest, 1325 Upshur St. NW. Patients would have to obtain service at nearby clinics or from private physicians through Medicaid.

At yesterday's press conference, Barry tried to inject a note of uncertainty into the closing by saying the proposed locations were only staff recommendations. When pressed on his intentions, however, he insisted that three clinics would be closed.

Barry said that the 216 uniformed police positions could be eliminated, like most others in city government, through attrition. Lower-paid civilians would replace officers now doing desk jobs, he said, and the net result would be the same degree of police presence on the street.

Housing was at the head of a list of 10 project areas spotlighted by the mayor as the "new directions" in city government. Barry said he has increased spending in the housing field by 114 percent above the level it was two years ago.

The proposed 14.1 million outlay for housing next year would include $2 million to help 200 renters purchase their homes through right-of-first-refusal procedures, and $2 million for the city to purchase and renovate 200 units for subsequent rental to low and middle income families. Nearly 1 million would be spent to repair abandoned housing units, whose owners would later have to reimburse the city.

The budget would continue for the second year a suspension of bookmobile service by the city library due to lack of funds. The library would, however, institute a new system to help reduce theft and loss of books. The budget would increase by 20 percent the funding for arts projects and double the amount of money spent on women's programs.

Barry also would provide money to beef up the staff of the agency that enforces the city's rent control law. The mayor proposed an increase of 22 positions for the office of the corporation counsel, including 14 lawyers, which would bring the number of attorneys in the office up to the level of eight years ago. CAPTION: Picture 1, Northwest Health Center, 13th and Upshur streets, would be closed if mayor's proposed budget is adopted, By Margaret Thomas -- The Washington Post; Picture 2, Budget proposals include $3.7 million to renovate homes at the East Capitol Dwelling housing project, By Douglas Chevalier -- The Washington Post