The Arlington County Board yesterday approved a $265.4 million budget for the next fiscal year that funds a 9.5 percent increase in school spending while still providing for substantial capital improvements and tax cuts for owners of homes, motor vehicles and businesses.

"This is a year for school programs . . . The community indicated that it wanted to take big steps forward in school spending," said Board Chairman John G. Milliken as the board enacted the budget.

The board voted to increase to $59 million the county's share of the school system's overall $83.4 million budget. That represents a 9.5 percent increase over the current budget and is the largest item in the county's fiscal 1986 budget.

The 4-to-1 vote broke along party lines, with the county board's only Republican member, Michael E. Brunner, dissenting in protest of what he said was a budget "balanced too heavily in favor of more spending" instead of larger tax cuts.

Brunner failed to get a second for his motion yesterday to slice 20 cents off the current personal property tax rate of $4.75 per $100 assessed value.

The board then unanimously cut 10 cents off the tax, which covers motor vehicles, boats, office equipment and airplanes. Because Arlington assesses those differently from other Virginia localities, the effective rate will be $4.19 per $100, one of the lowest in the area.

The board last month cut the real estate tax rate, the county's largest single revenue source, by 2 cents to 95 cents per $100 assessed value, the lowest in the area. The board's four Democrats then rejected Brunner's request for a 4-cent cut, saying they wanted to cut other taxes and fund more county and school program improvements.

Another $1 million in business license taxes was cut yesterday to meet a state mandate for reductions, bringing the total county tax cuts to $4 million.

Those revenue losses, budget director Mark Jinks said, have been offset by a substantial increase in commercial assessments and an almost $6 million surplus from the current fiscal year, which ends June 30.

The $265.4 million county budget is an 8 percent increase over the current year, and includes a $219.3 million general fund, supported primarily by county taxes, to run the county and the school system.

" It is a continuation of good services and bargain tax rates," Milliken said of the budget. It calls for a 4 percent cost-of-living increase for county and school employes and $10.4 million for capital improvements.

The capital spending budget includes a $1.5 million set-aside fund for improvements in the Rosslyn-Ballston Metro corridor and money for a new Columbia Pike fire station site and improvements to the county's roads, jail and water and sewer treatment systems.

"I am particularly pleased with the funding for the school budget . . . which includes excellent improvements to the school system," said board member Mary Margaret Whipple. Both Whipple and Brunner, who supported the school funds, are former School Board members.

School Board Chairman Gail Nuckols said the schools would use the additional money to improve the science and computer programs, add an optional extra class period to the school day and expand both summer school and Saturday curriculum offerings.

In addition to cost-of-living pay raises, she said, the School Board would use the funds to increase the salaries of administrators, summer school and substitute teachers, and to boost longevity raises for senior teachers.

The new budget provides program improvement funds that board member Albert C. Eisenberg described as the county's "reaching out with a helping hand and a vulnerable heart."

They include money to expand programs aimed at curbing family violence, providing day care for the frail elderly, teaching English to foreign-born adults, improving housing developments and adding library resources. Also included are funds for more firefighters in Crystal City and for two parking violation officers for 700 new parking meters throughout Arlington.