RICHMOND -- Like Charles S. Robb a decade ago, Edwina (Eddy) Dalton is seeking elective office for the first time this year, and already friends and foes say she has her eye on higher places.

Dalton, the 51-year-old widow of Republican Gov. John Dalton, is challenging the state Senate's senior member, William F. Parkerson Jr., 67, in suburban Henrico County in the Nov. 3 election, and she's already being touted as a candidate for lieutenant governor in 1989.

When political novice Robb ran for that office in 1977, everyone predicted he would move directly to governor four years later, which he did, and then on to national office, which he might.

Although they are of different parties and philosophies, moderate Democrat Robb and conservative Republican Dalton share an important ingredient in politics: name recognition and star quality.

Even before U.S. Sen. Paul S. Trible Jr. (R-Va.) left his news conference here last Monday, at which he hinted he might seek the GOP gubernatorial nomination, party loyalists in the audience were salivating at the prospect of a Trible-Dalton ticket in 1989.

Dalton's name also has surfaced as a possible running mate with another potential gubernatorial candidate, J. Marshall Coleman.

So strong is the support for Dalton that some say she will be wooed for statewide office even if she loses to Parkerson, so long as she makes a good showing.

On that score, there is little doubt.

Since shortly after she announced her candidacy in March, polls have shown Dalton leading Parkerson, who has been in the state Senate since 1964.

"She's the most attractive candidate we could put up," said M. Boyd Marcus Jr., administrative assistant to Rep. Thomas J. Bliley Jr. (R-Va.), who is advising her.

Parkerson is ahead, however, in raising money in what is already the most expensive legislative race in Virginia history.

As of Aug. 10, the most recent reporting date, the two candidates together had raised more than $630,000, with Parkerson enjoying a $100,000 advantage -- $367,838 to $268,291.

The old record was set four years ago by freshman Sen. J. Granger Macfarlane (D-Roanoke), who spent $123,000, of which $92,000 was his own money.

The next reporting date is eight days before the November election, and by then some believe Dalton and Parkerson together will have raised and spent $1 million.

The battle in the 12th senatorial district stands out in a lackluster election year, in which no federal or statewide candidates are on the ballot and even the question of whether Virginia should operate a lottery appears incapable of exciting the electorate.

Dalton is not the only woman seeking a seat in the all-male state Senate, which in its long history has had only two women members -- Eva F. Scott (R-Amelia) and Evelyn M. Hailer (D-Norfolk) -- both of whom served earlier this decade.

Del. Yvonne B. Miller (D-Norfolk), running for the 5th District seat being vacated by censured Democrat Peter K. Babalas, is favored in her bid to become the first black woman to serve in the 40-member Senate.

Other women given a chance at breaking into "the club" are McLean attorney Bobbie Kilberg, a Republican opposing Sen. Clive L. DuVal 2d in the 32nd District; Fairfax businesswoman Emilie Miller, a Democrat making a second try at unseating Republican John W. Russell in the 34th District, and Joan Girone, a Republican supervisor in Chesterfield County who is running as an independent in the 11th District after losing the GOP nomination to incumbent Robert E. Russell in what Girone contends was a rigged caucus.

Leaders of both parties say there is likely to be little change in the present lineup, in which Democrats control the Senate 31 to 9, and the House 66 to 33, with one independent.

"We're not going to take control of either chamber this year, but we could make major gains," said state GOP Chairman Donald W. Huffman.

Steve Haner, the GOP's communications director, added that the Republicans hope to pick up three to five seats overall.

"Anytime you have the majority we have in both houses, it's hard to do much better. We're happy to maintain the status quo," said Susan Swecker, executive director of the state Democratic Party.

Nearly half of the 40 Senate seats are uncontested, ensuring the reelection of 17 Democrats and two Republicans, including Northern Virginia Democrats Charles J. Colgan of Prince William, Richard L. Saslaw of Fairfax and Charles L. Waddell of Loudoun, and Republican Wiley F. Mitchell Jr. of Alexandria.

In the House, 46 Democrats and 22 Republicans are unopposed, including Northern Virginia Democrats David G. Brickley, Gladys B. Keating, Mary A. Marshall and Kenneth R. Plum, and Republicans James H. Dillard II, Robert E. Harris, Frank Medico and Kenneth B. Rollins.

By consensus, the most hotly contested Senate races, other than Parkerson-Dalton, involve incumbent Democrats Edward R. Houck of Spotsylvania, William T. Parker of Chesapeake and DuVal in Fairfax; incumbent Republicans Robert E. Russell of Chesterfield and John W. Russell of Fairfax, and a seat being vacated by Democrat James P. Jones of Abingdon.

Of those, Parker, Houck and Robert Russell are considered the most vulnerable.

Parker, a self-made millionaire builder, lost a vital labor endorsement to his Republican challenger, lawyer Mark Earley.

Freshman Houck, an assistant high school principal, is being outspent by Fredericksburg developer-lawyer William J. Vakos, who has accused Houck of voting to raise taxes and his own salary, and being beholden to the Virginia Education Association. Houck said Vakos is distorting his record.

The Republican nominee for Jones' seat, William C. Wampler Jr., is the son of the district's longtime congressman and, as such, has a name recognition advantage over his Democratic opponent, lawyer-businessman John S. Bundy.

Other GOP senators with serious opposition are Kevin G. Miller in the Shenandoah Valley, who is being challenged by William C. Chase Jr., chairman of the Culpeper County Board of Supervisors, and A. Joe Canada Jr. in Virginia Beach, whose Democratic opponent is Moody E. (Sonny) Stallings, a lawyer whose well-financed campaign has been aided by appearances by Gov. Gerald L. Baliles and Robb, a fellow Marine Vietnam veteran.

In the 100-member House, incumbents viewed as having serious opposition include Leslie L. Byrne (D-Fairfax), who may be outspent by Republican A. Strode Brent, an Annandale lawyer; John A. Rollison III (R-Prince William), who faces a rematch with George Dowd of Dumfries; Franklin M. Slayton (D-South Boston); Ford C. Quillen (D-Gate City); G.C. Jennings (D-Marion), who always has a fight; Kenneth E. Calvert (R-Danville), whose district is a GOP stronghold but where Democrats have raised more than $25,000 trying to help Calvert's opponent, Whittington W. Clement, and Royston Jester III (R-Lynchburg), who faces a well-organized opponent in Edward (Ted) R. Harris Jr.

Open House seats include close contests in Fairfax, where Jane H. Woods is trying to retain for the GOP the seat being vacated by Stephen E. Gordy against Democrat Jeffrey J. Fairfield of Herndon, who came close to winning in 1985; and in Wise County, where Norton attorney J. Jack Kennedy, who defeated incumbent James W. Robinson in the Democratic primary, is bringing in Sen. Albert Gore Jr. of neighboring Tennessee to help in Kennedy's race against Republican Bonnie Elosser, a teacher.

The Parkerson-Dalton contest pits his experience and clout against her energy and solid Republican credentials. Party affiliation could be the difference. The suburban Richmond district gave GOP gubernatorial nominee Coleman 60 percent of the vote in his losing race against Robb in 1981, and preferred Wyatt B. Durrette over Baliles in 1985 by 58 to 42 percent.

Beyond party and style, Parkerson and Dalton offer few alternatives. At a debate late week, both favored tougher penalties for drug dealers, parental notification of students seeking abortions or using drugs, the return of any windfall from changes in the federal tax code to the taxpayers, and a 65 mph speed limit. Both bemoaned rising insurance rates and acquired immune deficiency syndrome, and opposed abortion and higher taxes.

"I'm conservative and I'm experienced," said the soft-spoken Parkerson, who emphasized that his six terms in the Senate have helped him become its president pro tempore and the only Richmond-area senator on the Finance Committee.

"Seniority is good, but sooner or later it ends, with retirement or defeat," countered Dalton, who noted that her late husband, along with Baliles and former governor Mills E. Godwin, all got to the legislature by ousting incumbents.