Virginia voters recovering from a year of electioneering by gubernatorial candidates were treated today to the opening of what is expected to be an equally intensive battle to replace retiring Republican William L. Scott in the U.S. Senate.

Republican State Sen. Nathan H. Miller, a 34-year-old Shenandoah Valley lawyer and conservative, announced that he will seek the GOP nomination at the party convention next June.

Miller is expected to be opposed by three far better known Republicans in what could become the most spirited contest ever for a GOP nomination in Virginia. The other three are former state GOP chairman and unsuccessful 1969 attorney general candidate Richard D. Obenshain, former Gov. Linwood Holton and former Secretary of the Navy John L. Warner.

Until the late 1960s. Republican nominations for statewide office were prizes of little value. Since 1966, however, Democrats have won only four of 16 statewide elections - including presidential contests - and have slipped to minority of four in the state's 12-member congressional delegation.

Republicans scored their greatest electoral success of the country on Tuesday with the easy election of Lt. Gov. John N. Dalton as governor and State Sen. J. Marshall Coleman as attorney general. These victories have the effect of making the 1978 GOP Senate nomination all the more desirable to the candidates who made up their mind to seek it weeks or even months ago.

Miller is a quiet legislator who is well liked in the party, counsel to the state GOP and chairman of the state convention last June. But he admitted today that he will have to work hard to catch up with his GOP opponents. They are expected to announce in the next few weeks.

Two Fairfax Democrats state Del. Carrington Williams and former county Board of Supervisors Chairman Frederick A. Babson, have already announced their intentions to seek the Democratic nomination in the party primary next June and at least six others are listed as possible Democratic candidates.

Best known of the potential Democratic candidates is former Attorney General Andrew P. Miller, who spent a record $1.1 million in an effort to win his party's gubernatorial nomination this year, but lost narrowly to former Lt. Gov. Henry E. Howell, who in turn was defeated by Dalton on Tuesday.

The other Democrats who have been mentioned as possible candidates are state Sen. Hunter B. Andreas of Hampton, former Fairfax Supervisor Rufus Philips, state Sen. Clive L. DuVall II of Fairfax. Rep. Herbert E. Harris and state Sen. James T. Edmunds of Lunenburg County.

Among the Republicans, Obenshain and Miller are somewhat more conservative than are Warner and Holton, but the ideological range is more narrow than it is among the potential Democratic candidates. The chances for th GOP candidates to win the nomination now are being judged in the light of their relationships with local party officials throughout the state and their presumed ability to attract supporters next spring to the city and county mass meetings that will choose convention delegates.

Obenshain in regarded as having the highest standing with the orthodox conservatives who controlled Virginia Republican conventions before this year.

He was able to win the party chairmanship over Holton's opposition during Holton's term as governor from 1970 to 1974. However, Obenshain's image as a master of party conventions was tarnished this year when independent-minded delegates chose as a lieutenant governor candidates state Sen. A. Joe Canada of Virginia Beach. Obenshain and other party leaders, including Dalton, had wanted former state secretary of finance Walter W. Craigie Jr. of Richmond.

Coleman also scored a mild upset at the convention by winning the attorney general nomination over Del. Wyatt B. Durrette Jr. of Fairfax. These convention results give encouragement to Obenshain's opponents, especially Holton and Warner.

Holton alienated many party regulars during his term as governor, but he became Virginia's first Republican governor of this century, partly on the strength of an energetic campaign style. He has been hard to work recruiting support for his prospective Senate bid in recent weeks.

Warner and his wife, actress Elizabeth Taylor, have been piling up debts of political gratitude all over the state by attracting crowds and contributions to party fund-raisers. They were tireless campaigners for Dalton, Coleman and Canada.

The rapid succession of political campaigns in Virginia is beginning to boggle the minds of politicians as well as voters. Del. Gerald L. Baliles, a respected moderate Democrat from Richmond, recently proposed that the General Assembly consider shifting the election of state officers from odd-numbered years following presidential elections to even-numbered years between presidential contests.