While many school systems around the country are caught in a severe financial squeeze, Washington's public schools have started fall classes with a $7.7 million fix-up and shopping spree and have made plans to add several hundred more teachers, computers, and bilingual classes when the new fiscal year begins next month.

The shopping list, financed by surplus school funds for the budget year that ends Sept. 30, includes $600,000 for musical instruments, $500,000 each for typewriters and science equipment, $300,000 to repair school lockers, and $295,000 for security alarms.

School lunch prices, already the lowest in the area, are being reduced by 10 cents a meal, to 50 cents for elementary students and 60 cents for high schools, 15 to 35 cents less than in any local suburb.

Meanwhile, a $42 million budget increase for the new fiscal year is awaiting congressional passage without apparent opposition. With those funds, D.C. school officials are planning to add 275 teachers, hire enough clerical aides to help each teacher with paperwork at least three hours a week, restore driver education, spend $1.1 million on computer equipment for the city's 183 local schools, and buy $912,000 worth of new buses for handicapped students.

The school system also is planning to spend $500,000 for 180 students in a Spanish-English high school program that lost its federal CETA grant.

The system's left-over money for the current fiscal year amounts to $7.7 million -- $1.2 million from funds saved when a decline in oil prices cut heating bills, and $6.5 million left after a large federal subsidy paid school lunch costs for which local funds had been budgeted.

The request to shift this money for end-of-year purchases was approved routinely two weeks ago by the House D.C. appropriations subcommittee and is expected to clear a Senate subcommittee soon.

"We need all these things to strengthen our school programs," said Arthur G. Hawkins, associate superintendent for financial management.

This fall's relative prosperity in the D.C. schools, which includes expenditures of $212,000 for sports equipment and $120,000 for pianos at the Duke Ellington School of the Arts, is in sharp contrast to the fiscal problems that marked the opening of school for the past two years.

In September 1980, the school system cut 819 jobs, including 672 teachers, about 10 percent of its teaching staff. The system then was caught in the District's general financial crisis caused by years of deficit spending.

Last fall's opening was clouded by threats of a six-day unpaid furlough for all school employes. It was averted just two weeks before the start of classes when Mayor Marion Barry switched $2.8 million to balance the school budget.

"We were functioning under austere conditions for the past few years," said Hawkins. "But now under the new leadership of superintendent Floretta McKenzie you can see the turn-around. It's going to be a good year."

D.C. school finances for the coming fiscal year, which begins Oct. 1, were boosted by decisions last winter by the City Council -- five of whose 13 members were then planning to run for higher office. After receiving reports of higher-than-expected tax revenues for fiscal 1981, the council voted to cut back repayment of the District's long-term debts and to give more money to the schools.

Barry originally sought a far more modest increase in the school budget, tied to falling enrollment and lower inflation. After vigorous lobbying by parents, he changed his mind and endorsed the "full funding" budget voted by the council.

Included in this year's spending package is $116,876 for new D.C. history textbooks, $150,000 for printing new report cards, parent handbooks, and curriculum guides, and extra money for equipment and supplies for three of the District's high schools with special programs -- $63,000 for the Banneker academic high, $106,000 for the special science and math program at Ballou, and $261,000 for Ellington, including the pianos.

There is also $800,000 for painting, roofing, and other repairs and minor building improvements, which had been deferred.

The new teachers in the budget for the 1983 fiscal year, which starts Oct. 1, will be used mostly to cut average class size to 25 students in elementary grades and 26 in junior and senior highs. With enrollment expected to drop by 3,700 this fall, average class size will be lower than it was in 1979-80, the year before the major layoffs.

Even before this improvement, classes last year were smaller than they had been in the mid-1970s. Overall, from the fall of 1976 to the fall of 1981, enrollment in D.C. public schools dropped by 25 percent to 94,425, while the teaching staff declined by 20 percent to 5,834.

According to the most recent data available from the National Center for Education Statistics, per-pupil spending in District schools was higher than that for any state except Alaska in fiscal 1981, the year of the District's budget crisis. In 1980-81, D.C. spending per pupil was considerably above Fairfax and Prince George's, slightly below Montgomery, and well below Alexandria and Arlington.

Reports from around the country indicate staff cutbacks and tight budgets in many school systems, including big cities such as Chicago, Detroit, and St. Louis, where recession has hit hard. In the Washington suburbs most school systems have only slight budget increases. In Prince George's, which is facing a severe squeeze because of a tax limit in the county charter, about 450 teachers have been laid off.

For next year the District expects a $7.6 million cut in federal school aid. But the increase in local money is so great that the city can continue all the federally funded programs it wants as well as make substantial improvements. CAPTION: Picture, Superintendent Floretta McKenzie has requested $336.5 million for fiscal year 1984. By Gerald Martineau -- The Washington Post