RICHMOND, JAN. 15 -- After three days of anxiety, Northern Virginia school officials got their first look today at projections of how much state financial aid they would get under Gov. Gerald L. Baliles' budget proposal.

For the most part, the news was good.

Fairfax County schools would receive $386.4 million for 1988-90. While that represents a jump of $35.7 million from the state's contribution in the current two-year budget, it is a somewhat smaller rate of increase than Fairfax has received in the past.

"It could have been worse," said John P. Hess, deputy superintendent for finance for Fairfax's school system. He said that Fairfax school officials needed to "impress upon" Northern Virginia lawmakers the importance of guarding the money from fiscal raids by downstate lawmakers.

Of every $1 spent to educate a student in Fairfax public schools, about 20 cents comes from state funds. Most of the remaining money comes from politically sensitive local real estate taxes.

Fairfax officials and other Northern Virginians had been worried that Baliles' new financial aid formula, intended primarily to help poorer, mostly rural schools, might result in the same or only marginally higher funding for wealthier schools in urban areas.

But Baliles' proposal included a bonus for Northern Virginia that recognizes what he called the "cost of competing" for top-notch teachers in the Washington area. That bonus made up for other reductions in state aid under a revised funding proposal.

Fairfax, with nearly 130,000 students, has by far the largest school system in Virginia, and one of the 10 biggest in the nation.

In the fiscal year starting July 1, the county would receive $1.8 million less in state funds than the $190.7 million Superintendent Robert R. Spillane had estimated.

There was no word today on whether Spillane would cut his spending proposal accordingly or ask the county's Board of Supervisors to make up the shortfall.

Prince William County's rapidly growing schools, which will receive $141.9 million from he state in the current two-year period, would get $180.1 million for 1988-90 -- one of the sharpest increases in the state.

Loudoun County schools, which got $39.1 million in 1986-88, would receive $43.5 million in the coming two years.

Alexandria and Arlington schools would receive only marginal increases, a situation both have faced in recent years because of their comparatively stable enrollments.

Prince William School Superintendent Edward L. Kelly said the governor's plan "treats us very fairly" and will be "necessary if we're to accommodate the growth we're going to have."

Kelly added: "I hope it holds up. After you've been through one of these legislative sessions, you know it's not over till it's over."

Several downstate lawmakers have already suggested they may attempt to cut the bonus for Northern Virginia that Baliles included in his new funding formula. Northern Virginia school officials said they will vigorously fight such attempts.

Prince William's student enrollment, about 39,000, grew by 3 percent this year and is expected to continue to expand at the same rate every year until 1995.

Staff writer Alice Digilio contributed to this report.