Northern Virginia legislator Vivian E. Watts, who played a key role in drafting legislation that will funnel more money to the state's urban areas, was picked today by Gov.-elect Gerald L. Baliles as his secretary of transportation and public safety.

Watts, 45, an Annandale Democrat, is the first Northern Virginian to be given a cabinet-level authority over the state's often independent and powerful highway agency. Her $73,571-a-year position in Baliles' cabinet also will place her over the state's troubled prison system.

Baliles today praised Watts, a four-year member of the House of Delegates, for her "leadership role in the General Assembly on transportation issues," and her "keen mind, intellectual depth and unusual sensitivity . . . . This lady's a leader."

Watts said she would choose deputies for transportation and corrections with "line expertise," but dodged a question about whether she would urge Baliles to reappoint State Highway Commissioner Harold C. King.

Some members of the outgoing administration of Gov. Charles S. Robb have said privately that unless King is replaced with someone more attuned to the state's changing transportation needs it could be difficult for anyone, including Baliles, to have a major impact on highway issues.

Watts' appointment stunned Northern Virginia legislators and threw Fairfax County Democrats and Republicans into a hurried search for possible candidates to replace her in a special election, expected to be called prior to the Jan. 8 start of the 1986 General Assembly.

"We're going to miss her tremendously," said state Sen. Clive L. DuVal (D-Fairfax). "She was a valuable member of the delegation. I hate to lose her in that capacity."

One local official who hailed Watts' selection was Fairfax County Supervisor Audrey Moore (D-Annandale). She said that having a friend in the Virginia transportation agency will "be a great advantage to Northern Virginia.

"She fully understands our problems," Moore said. "At least it won't be someone going in who has no concept of what is going on up here."

Asked if she would give special attention to the Washington area's Metro system and highways, Watts said she is "comittted to a fully integrated approach" to Northern Virginia's transportation needs.

One of her first goals, however, she said, will be to see if the state can provide $5 million for insurance for a proposed commuter train service that would connect Manassas and Fredericksburg with Washington.

In the troubled corrections system, which has seen five directors in the last four years, Watts said she will look to "set new directions. There is much to work on, in physical needs and personnel."

Watts will direct 14 agencies, with more than 20,000 employes, assigned to highways, ports, prisons, motor vehicles, state police, parole, alcoholic beverage control, aviation and military affairs agencies. She will succeed Andrew B. Fogarty, who will become vice president for administration at the College of William and Mary.

Watts said she "decided with great difficulty, it was very wrenching" because it disrupted her goal of serving 20 years in the legislature.

"I would not have been tempted by any other position within the cabinet," she said at a news conference at the state Capitol.

Watts also had been mentioned as a possible Democratic candidate for Congress from Northern Virginia. Republican Rep. Stan Parris today praised Watts' selection as an "excellent choice, a very competent, capable, forward-looking member of the General Assembly."

Although Baliles previously had discussed the position with Fairfax County Executive J. Hamilton Lambert, he said there was no special effort made to award the position to a Northern Virginian.

Watts, a graduate of the University of Michigan, has lived in Virginia for 22 years. She came to elective politics through community work, including serving two years as president of the Fairfax area League of Women Voters in the mid-1970s.

She was elected in 1981 to the House, where she has been vice chairman of the Committee on Taxation of Public Utilities, and a member of the Finance, Labor and Commerce committees.

For the last two years she has been employed as a researcher for Arthur Young & Co.

Watts said she will commute to Richmond, returning to Annandale on weekends, "unless my husband wants to meet me at a good trout stream" someplace else in the state.

Baliles today also named a number of staff appointments, including:

Darrel Martin, 40, who was Baliles' campaign manager, to the new position of executive assistant for the office of strategic planning, at a salary of $50,000 a year; Philip F. Abraham, 28, senior assistant for policy, $39,000; Christine O. Bridge, 35, press secretary, $38,000; G.C. Morse, 36, speechwriter, $38,000; Alan D. Albert, 29, special assistant for policy, $35,000; Meredith Strohm, 33, special assistant to chief of staff David McCloud, $35,000, and Valerie Watkins, 31, special assistant for policy, $35,000.