Stafford County supervisors, three of whom face reelection this year, began searching this week for ways to avoid what would amount to about a 16 percent increase in the county's property taxes to finance a proposed $41.4 million budget.

The supervisors were scheduled to tackle the thorny issue for the first time last night. They have scheduled public hearings for April 11 and 12 and hope to adopt the fiscal 1983-84 budget by the end of April.

Most of the supervisors have indicated that taxes must be cut in some fashion: the debate likely will concern how much the county can cut and still provide expected services to residents and salary increases to employes.

Stafford County taxpayers recently learned that new property assessments had jumped 30 percent over the last assessments conducted in 1979. With the assessment increases in mind, supervisors were told that just to keep taxes at the same level as last year they would have to lower the tax rate to $1.16 per $100 assessed property value, down 29 cents from this year's rate of $1.45.

County Administrator Richard Bain's $41,367,229 budget includes a proposed tax rate of $1.35 per $100 assessed value.

"Personally, I won't consider anything lower than $1.25," said board Chairman Charles Wandrick, North Stafford's representative from the Griffis-Widewater District.

Wandrick's board term expires this year, as does the term of Rockhill Supervisor G.W. Embrey and George Washington Supervisor Alvin Y. Bandy.

Embry has been the most outspoken opponent to the tax increases; he and Wandrick have been longtime adversaries on the board and are likely to differ on what the tax rate should be. Embry and two other supervisors, Bandy and E. Lloyd Chittum of the Hartwood District, voted against a resolution to advertise the public hearings for the proposed budget, saying the proposed budget was not the one they wanted to take before the taxpayers.

"I don't think you can advertise until we go through the budget. We're going to cut it to the bone," Embry said when the board first saw the figures.

Wandrick said the budget could be slashed considerably by cutting the school system's budget. "Sure I can cut the budget. Just by cutting the pay raises to the teachers, I can cut it by $1.25 million," he said.

Bain and School Superintendent Andrew G. Wright have proposed a $26,572,454 budget for Stafford schools. Teachers would receive a 10 percent salary increase, while the school system's staff would get a 4 percent raise. The 10 percent raises would amount to $1.1 million in additional costs. Total school system raises would come to between $1.25 million and $1.3 million.

County employes also would receive a 4 percent pay raise in Bain's proposed budget. That would cost an additional $75,000.

In Bain's 26-page budget report, he asked that county employes begin paying a portion of their insurance premiums. He stated that Blue Cross-Blue Shield coverage would increase from 20 to 30 percent in the next year.

Bain wants county employes to pay $83.20 a year toward a single subscriber's premium and $208 for a subscriber and his family. The county has never charged its employes for the insurance.

Stafford employed 1,211 persons in 1982, of which 970 were school system personnel and 241 were administration and other staff workers.

The Board of Supervisors is likely to suggest additional measures to cut the budget because of mounting opposition by taxpayers to any increase in tax levies.

During last week's meeting, Chittum was given a petition signed by 100 constituents calling for a 90-cent tax rate.

"They're serious about this. These are just from the Hartwood District," Chittum said.

In North Stafford, a citizens' group has announced its plan to initiate what it calls "a Proposition 13-type thing" to lower taxes.

The public hearings on the proposed budget at are scheduled for 7:30 p.m. April 11 at Stafford Senior High School and 7:30 p.m. April 12 at North Stafford High School.