Fairfax County Executive J. Hamilton Lambert proposed a $615.7 million budget yesterday that calls for the smallest percentage increase in spending in 25 years and no increase in the county tax rates.

The assessed value of most detached, single-family homes is expected to remain the same or drop slightly under the proposed 1984 fiscal budget, meaning property taxes for some homeowners will decline. Overall, taxes for owners of single-family homes, condominiums and town houses are expected to rise an average 1.4 to 1.5 percent.

The estimated assessed value of a typical Fairfax house will rise from $99,045 to $101,521, for an increase in property taxes from $1,455.96 to $1,492.36, according to Lambert's proposed budget.

In addition, the typical household will pay $203.75 in personal property taxes, $156.90 in sales taxes, and $86.76 in consumer utility taxes, for a total of $1,939.77, compared to $1,875.17 in fiscal 1983. Direct county expenditures for nonschool spending would average $1,011.53 per household.

He called the budget "prudent," adding that it is "sensitive" to the needs of county residents but avoids costly new projects or large staff increases. The budget proposal calls for 44 new positions, the lowest number in the last 10 years, Lambert said.

Lambert said that no major cuts were made in programs and that some new projects were funded. "I cried a lot," Lambert said of his efforts to encourage agency officials to keep their budget requests down. "We let them know that we wouldn't accept" huge staff increases.

The budget must be approved by the Board of Supervisors. Supervisor Thomas M. Davis (R-Mason) said he expects the board to ratify it without major changes, particularly because Lambert has recommended maintaining the property tax rate of $1.47 per $100 of valuation.

The county's $615.7 million budget proposal is 5.3 percent higher than the fiscal 1983 budget and below the board's self-imposed ceiling of a 5.85 percent increase. If items such as the expenditures of bond proceeds, the cost of fee-supported sewer and refuse services are included, the budget hits $1 billion for the first time in the county's history.

Major increases include a 3 percent cost-of-living increase for county employes costing $5.1 million, individual merit increases of about 2 percent for fewer than 40 percent of county employes costing $2.5 million, and a $3.3 million increase resulting from major changes in health insurance and retirement contributions.

The proposed budget includes funding for new Tysons Corner and Pohick libraries and a staff of 11, expanded facilities for the Park Authority and seven new staff positions, five new day-care centers and 11 new positions, and a new computer dispatch system for police, fire and rescue.

Programs slated to get increased funding include public safety, up 2.2 percent; parks and recreation, up 8.6 percent, and health and welfare, up 0.2 percent. The judicial administration budget is to be cut 15.7 percent due to one-time costs in fiscal 1983 for equipping the new judicial center.

The county's administrative budget is to be cut by 0.2 percent. The county expects to save some money because of the tighting of federal and state eligibility requirements, which caused a 3.2 percent decline in welfare cases during the first six months of fiscal 1983.

Lambert praised the School Board for keeping the increase in its proposed $449.5 operating budget to 5.1 percent. Because of a decline in revenue from other sources, the county's present $296.2 million contribution to the school budget would have to be increased by 5.85 percent.

State and federal funds make up about 6.5 percent of the budget and the county estimated it would receive $39.73 million in such contributions. But Lambert said he had "no idea" how anticipated federal cuts would eventually change the budget. Congress is now working on its fiscal 1984 budget.

Lambert said he had not had time to analyze the impact of the recently passed state budget. But he said the reduction in state aid would be in the "thousands rather than the millions" anticipated at the beginning of the year.