The Fairfax County School Board this week began what is likely to be its most contentious task this year: consideration of the superintendent's proposed $589.2 million budget for 1986-87.

The record blueprint submitted Monday by Superintendent Robert R. Spillane would provide a 4 percent cost-of-living raise for all school employes, spend $2.7 million on staff and equipment to accommodate the baby boomlet in the county's classrooms, and begin a costly three-year program to improve use of computer-aided instruction. The budget would increase 7.1 percent.

Early reaction was mixed to the proposed spending plan for Virginia's largest school system, a sign that this year's budget battle could be fiercer than usual.

Teachers and their PTA allies are dissatisfied with Spillane's proposed salary increase; last year, the issue was settled before budget hearings began. Questions already have been raised about the classroom computer plan and proposed spending to improve achievement by minority students.

"Last year, there was not a lot of disagreement," said School Board member Laura I. McDowall of Annandale. "The budget will consume a lot more thought and energy this year."

Already, 30 people have signed up to testify at the two nights of public hearings scheduled Feb. 3 and 4, and many more are expected to do so. Daunted by memories of past sessions that dragged into early morning, the School Board tonight is scheduled to consider new time limits on speakers.

The proposal, scheduled for a vote Jan. 23, would restrict each individual to three minutes and each representative of a county organization to five minutes, the same rules that apply to the board's regular biweekly meetings. Currently, individuals are limited to five minutes and organization spokesmen to 10 minutes at public hearings. Supporters say the new rule would allow more people to speak.

The board has scheduled budget work sessions Jan. 16 and Feb. 6. It will make tentative decisions Feb. 11, and adopt its final budget Feb. 19. The spending plan then goes for final approval to the Board of Supervisors, which is scheduled to adopt its budget in April.

School Board Chairman Mary E. Collier said her initial reaction to the budget is approval, particularly of Spillane's proposals for smaller kindergarten classes and more elementary school art instruction. "Overall, I think he focused the resources into the classroom and addressed the priority the School Board held near and dear," she said. "We're going to sit and listen to the community now."

School Board member Frank Francois questioned Spillane's proposal for only a small increase in spending for minority achievement improvement, noting that the issue is an official School Board priority.

"I would like for someone to tell us why this increase is so small," he said.

Donna Caudill, president of the Fairfax Education Association, said her members are disappointed in Spillane's failure to increase his salary offer and "teachers are looking for leadership on the part of the School Board in terms of teacher salaries." FEA and the Fairfax County Federation of Teachers are staging a "work-to-the-rule" job slowdown to protest the offer. Teachers are prohibited by law from striking.

But Collier said an almost-complete analysis by School Board staff appears teachers' claims they have lost money to inflation over the past decade. "They have done better in relation to inflation than county residents or civil servants," he said. "At least in the past, the county has done a lot to support its teachers."

McDowall, like Collier, was pleased with Spillane's proposal to shrink kindergarten class size from a maximum of 30 to a ceiling of 28, although disappointed more could not be done to reduce class sizes elsewhere. Spillane said there are not enough empty classrooms to do so.

McDowall questioned "the increase in the number of noninstructional positions" in the budget. She said she does not buy the idea that there is bureaucratic bloat in the school system, "but I want to make sure we need all those positions."

The School Board is to hear the details tonight of the proposal to spend nearly $3 million to improve computer-aided instruction in writing, problem-solving and science.

Brenda Z. Greene, cochairman of the county superintendent's community advisory committee, and Pat Hanlon, chairman of the PTA's budget committee, expressed doubts about the proposal to commit the schools to a three-year plan.

"It's expensive and there are a lot of questions about whether we're far enough along in evaluating what we've already done to go ahead," Hanlon said.

Hanlon said the PTA also will press for funding to replace aging school buses. Spillane said he would ask the supervisors to replace 77 buses dating back to 1973 and 1974 if money is available, but did not include the request in his budget.